The boundedness on Triebel-Lizorkin spaces of oscillatory singular integral operator T in the form e^i｜x｜^aΩ（x）｜x｜^-n is studied,where a∈R,a≠0,1 and Ω∈L^1（S^n-1） is homogeneous of degree zero and satisfie...The boundedness on Triebel-Lizorkin spaces of oscillatory singular integral operator T in the form e^i｜x｜^aΩ（x）｜x｜^-n is studied,where a∈R,a≠0,1 and Ω∈L^1（S^n-1） is homogeneous of degree zero and satisfies certain cancellation condition. When kernel Ω（x＇ ）∈Llog＋L（S^n-1 ）, the Fp^a,q（R^n） boundedness of the above operator is obtained. Meanwhile ,when Ω（x） satisfies L^1- Dini condition,the above operator T is bounded on F1^0,1 （R^n）.展开更多
In this paper, we will prove the Triebel-Lizorkin boundedness for some oscillatory singular integrals with the kernel （x） satisfying a condition introduced by Grafakos and Stefanov. Our theorems will be proved under...In this paper, we will prove the Triebel-Lizorkin boundedness for some oscillatory singular integrals with the kernel （x） satisfying a condition introduced by Grafakos and Stefanov. Our theorems will be proved under various conditions on the phase function, radial and nonradial. Since the L p boundedness of these operators is not complete yet, the theorems extend many known results.展开更多
The authors considered non-convolution type oscillatory singular integral operators with real-analytic phases. A uniform boundedness from HKp to Hp of such operators is established. The result is false for general C p...The authors considered non-convolution type oscillatory singular integral operators with real-analytic phases. A uniform boundedness from HKp to Hp of such operators is established. The result is false for general C phases.展开更多
In this paper, we want to improve our previous results. We prove that some oscillatory strong singular integral operators of non-convolution type with non-polynomial phases are bounded from Herz-type Hardy spaces to H...In this paper, we want to improve our previous results. We prove that some oscillatory strong singular integral operators of non-convolution type with non-polynomial phases are bounded from Herz-type Hardy spaces to Herz spaces and from Hardy spaces associated with the Beurling algebras to the Beurling algebras in higher dimensions.展开更多
In this paper, by using the atomic decomposition of the weighted weak Hardy space WH;（R;）, the authors discuss a class of multilinear oscillatory singular integrals and obtain their boundedness from the weighted wea...In this paper, by using the atomic decomposition of the weighted weak Hardy space WH;（R;）, the authors discuss a class of multilinear oscillatory singular integrals and obtain their boundedness from the weighted weak Hardy space WH;（R;） to the weighted weak Lebesgue space WL;（R;） for ω∈A;（R;）.展开更多
In this paper, for the multilinear oscillatory singular integral operators TA1,A2,...Ar defined by TA1,A2,...,Arf（x） = p.v.∫R^n ^e^iP（x,y）Ω（x - y）/｜x - y｜^n＋M r∏s=1 Rms＋1（As;x,y）f（y）dy, n≥2 where P...In this paper, for the multilinear oscillatory singular integral operators TA1,A2,...Ar defined by TA1,A2,...,Arf（x） = p.v.∫R^n ^e^iP（x,y）Ω（x - y）/｜x - y｜^n＋M r∏s=1 Rms＋1（As;x,y）f（y）dy, n≥2 where P（x,y） is a nontrivial and real-valued polynomial defined on R^n×R^n,Ω（x） is homogeneous of degree zero on R^n, As（x） has derivatives of order ms in ∧βs （0〈βs〈 1）, Rms＋1 （As;x, y） denotes the （ms＋1）-st remainder of the Taylor series of As at x expended about y （s = 1, 2, ..., r）, M = ∑s^r =1 ms, the author proves that if 0 〈=β1=∑s^r=1 βs〈1,and Ω∈L^q（S^n-1） for some q 〉 1/（1 -β）, then for any p∈（1, ∞）, and some appropriate 0 〈β〈 1, TA1,A2,...,Ar, is bounded on L^P（R^n）.展开更多
We obtain appropriate sharp bounds on Triebel-Lizorkin spaces for rough oscillatory inte- grals with polynomial phase. By using these bounds and using an extrapolation argument we obtain some new and previously known ...We obtain appropriate sharp bounds on Triebel-Lizorkin spaces for rough oscillatory inte- grals with polynomial phase. By using these bounds and using an extrapolation argument we obtain some new and previously known results for oscillatory integrals under very weak size conditions on the kernel functions.展开更多
In this paper,the boundedness is obtained on the Triebel-Lizorkin spaces and the Besov spaces for a class of oscillatory singular integrals with Hardy kernels.
The boundedness on weighted local Hardy spaces h<sup>1,p</sup><sub>w</sub> of the oscillatory singular integral Tf（x）=∫<sub>R</sub><sup>n</sup> e<sup>iQ（x,y）&...The boundedness on weighted local Hardy spaces h<sup>1,p</sup><sub>w</sub> of the oscillatory singular integral Tf（x）=∫<sub>R</sub><sup>n</sup> e<sup>iQ（x,y）</sup>K（x,y）f（y）dy is considered when Q（x,y）=P（x-y）for some real-valued polynomial P with its degree not less than two.Also a sufficient and necessary condition on polynomial Q on R<sup>n</sup> × R<sup>n</sup> such that T maps h<sup>1,p</sup><sub>w</sub> to the weighted integrable function space L<sup>1</sup><sub>w</sub> is found.展开更多
In this paper, the authors prove that some oscillatory singular integral operators of non-convolution type with non-polynomial phases are bounded from the Herz-type Hardy spaces to the Herz spaces and from the Hardy s...In this paper, the authors prove that some oscillatory singular integral operators of non-convolution type with non-polynomial phases are bounded from the Herz-type Hardy spaces to the Herz spaces and from the Hardy spaces associated with the Beurling algebras to the Beurling algebras in higher dimensions, even though it is well-known that these operators are not bounded from the Hardy space H1(Rn) into the Lebesgue spaceL1(Rn).展开更多
In this paper, we obtain the boundedness of the parabolic singular integral operator T with kernel in L（log L） 1/γ,（Sn- 1 ） on Triebel-Lizorkin spaces. Moreover, we prove the boundedness of a class of Marcinkiewi...In this paper, we obtain the boundedness of the parabolic singular integral operator T with kernel in L（log L） 1/γ,（Sn- 1 ） on Triebel-Lizorkin spaces. Moreover, we prove the boundedness of a class of Marcinkiewicz integrals μΩ,q （f） from ｜｜f｜｜Fp^oq（Rn） into Lp （Rn）.展开更多
Let h, be a measurable function defined on R^＋ ×R^＋. Let Ω ∈ L（log L^＋）^υq （S^n1-1 × S^n2-1） （1≤ υq ≤ 2） be homogeneous of degree zero and satisfy certain cancellation conditions. We show that...Let h, be a measurable function defined on R^＋ ×R^＋. Let Ω ∈ L（log L^＋）^υq （S^n1-1 × S^n2-1） （1≤ υq ≤ 2） be homogeneous of degree zero and satisfy certain cancellation conditions. We show that the singular integral Tf（x1,x2）=p.v.∫∫R^n1＋n2 Ω（y′1,y′2）h（｜y1｜,｜y2｜）/｜y1｜^n1｜y2｜^n2 f（x1-y1,x2-y2）dy1dy2maps from Sp,q^α1,α2F（R^n1×R^n2）boundedly to itself for 1 〈 p, q 〈 ∞, α1, α2 ∈R.展开更多
In this paper, the authors establish the weighted (L^p, L^q) estimates for aclass of multilinear oscillatory singular integrals with smooth phases. Certain endpoint estimatesare also considered.
In this paper, we prove the Triebel-Lizorkin boundedness for the Marcinkiewicz integral with rough kernel. The method we apply here enables us to consider more general operators.
In this article,we study the boundedness properties of the averaging operator S_(t)^(γ) on Triebel-Lizorkin spaces F_(p,q)^(α)(R^(n))for various p,q.As an application,we obtain the norm convergence rate for S_(t)^(...In this article,we study the boundedness properties of the averaging operator S_(t)^(γ) on Triebel-Lizorkin spaces F_(p,q)^(α)(R^(n))for various p,q.As an application,we obtain the norm convergence rate for S_(t)^(γ)(f)on Triebel-Lizorkin spaces and the relation between the smoothness imposed on functions and the rate of norm convergence of S_(t)^(γ) is given.展开更多
In this paper, we consider the rough singular integral operators on product Triebel-Lizorkin spaces and prove certain boundedness properties on the Triebel-Lizorkin spaces. We also use the same method to study the fra...In this paper, we consider the rough singular integral operators on product Triebel-Lizorkin spaces and prove certain boundedness properties on the Triebel-Lizorkin spaces. We also use the same method to study the fractional integral operator and the Littlewood-Paley functions. The results extend some known results.展开更多
Though the theory of Triebel-Lizorkin and Besov spaces in one-parameter has been developed satisfactorily, not so much has been done for the multiparameter counterpart of such a theory. In this paper, we introduce the...Though the theory of Triebel-Lizorkin and Besov spaces in one-parameter has been developed satisfactorily, not so much has been done for the multiparameter counterpart of such a theory. In this paper, we introduce the weighted Triebel-Lizorkin and Besov spaces with an arbitrary number of parameters and prove the boundedness of singular integral operators on these spaces using discrete Littlewood-Paley theory and Calderon＇s identity. This is inspired by the work of discrete Littlewood- Paley analysis with two parameters of implicit dilations associated with the flag singular integrals recently developed by Han and Lu [12]. Our approach of derivation of the boundedness of singular integrals on these spaces is substantially different from those used in the literature where atomic decomposition on the one-parameter Triebel-Lizorkin and Besov spaces played a crucial role. The discrete Littlewood-Paley analysis allows us to avoid using the atomic decomposition or deep Journe＇s covering lemma in multiparameter setting.展开更多
Though the theory of one-parameter Triebel-Lizorkin and Besov spaces has been very well developed in the past decades, the multi-parameter counterpart of such a theory is still absent. The main purpose of this paper i...Though the theory of one-parameter Triebel-Lizorkin and Besov spaces has been very well developed in the past decades, the multi-parameter counterpart of such a theory is still absent. The main purpose of this paper is to develop a theory of multi-parameter Triebel-Lizorkin and Besov spaces using the discrete Littlewood-Paley-Stein analysis in the setting of implicit multi-parameter structure. It is motivated by the recent work of Han and Lu in which they established a satisfactory theory of multi-parameter Littlewood-Paley-Stein analysis and Hardy spaces associated with the flag singular integral operators studied by Muller-Ricci-Stein and Nagel-Ricci-Stein. We also prove the boundedness of flag singular integral operators on Triebel-Lizorkin space and Besov space. Our methods here can be applied to develop easily the theory of multi-parameter Triebel-Lizorkin and Besov spaces in the pure product setting.展开更多
文摘The boundedness on Triebel-Lizorkin spaces of oscillatory singular integral operator T in the form e^i｜x｜^aΩ（x）｜x｜^-n is studied,where a∈R,a≠0,1 and Ω∈L^1（S^n-1） is homogeneous of degree zero and satisfies certain cancellation condition. When kernel Ω（x＇ ）∈Llog＋L（S^n-1 ）, the Fp^a,q（R^n） boundedness of the above operator is obtained. Meanwhile ,when Ω（x） satisfies L^1- Dini condition,the above operator T is bounded on F1^0,1 （R^n）.
基金Supported by the National Natural Science Foundation of China (11026104, 11201103, 11226108)
文摘In this paper, we will prove the Triebel-Lizorkin boundedness for some oscillatory singular integrals with the kernel （x） satisfying a condition introduced by Grafakos and Stefanov. Our theorems will be proved under various conditions on the phase function, radial and nonradial. Since the L p boundedness of these operators is not complete yet, the theorems extend many known results.
文摘The authors considered non-convolution type oscillatory singular integral operators with real-analytic phases. A uniform boundedness from HKp to Hp of such operators is established. The result is false for general C phases.
基金Xu Jingshi is partially supported by the NSF of Hunan,China(01JJY3003)A project supported by Scientific Research Fund of Hunan Provincial Education Department(02C067)
文摘In this paper, we want to improve our previous results. We prove that some oscillatory strong singular integral operators of non-convolution type with non-polynomial phases are bounded from Herz-type Hardy spaces to Herz spaces and from Hardy spaces associated with the Beurling algebras to the Beurling algebras in higher dimensions.
基金supported by the National Natural Science Foundation of China(Grant No.11501233)China Postdoctoral Science Foundation(No.2015M572327)+2 种基金Humanities and Social Sciences Program of the Ministry of Education(No.15YJC630053)Natural Science Foundation of Anhui Province(No.1408085MA08 and No.1508085SMA204)Natural Science Foundation of the Education Department of Anhui Province(No.KJ2015A335 and No.KJ2015A270)
文摘In this paper, by using the atomic decomposition of the weighted weak Hardy space WH;（R;）, the authors discuss a class of multilinear oscillatory singular integrals and obtain their boundedness from the weighted weak Hardy space WH;（R;） to the weighted weak Lebesgue space WL;（R;） for ω∈A;（R;）.
文摘In this paper, for the multilinear oscillatory singular integral operators TA1,A2,...Ar defined by TA1,A2,...,Arf（x） = p.v.∫R^n ^e^iP（x,y）Ω（x - y）/｜x - y｜^n＋M r∏s=1 Rms＋1（As;x,y）f（y）dy, n≥2 where P（x,y） is a nontrivial and real-valued polynomial defined on R^n×R^n,Ω（x） is homogeneous of degree zero on R^n, As（x） has derivatives of order ms in ∧βs （0〈βs〈 1）, Rms＋1 （As;x, y） denotes the （ms＋1）-st remainder of the Taylor series of As at x expended about y （s = 1, 2, ..., r）, M = ∑s^r =1 ms, the author proves that if 0 〈=β1=∑s^r=1 βs〈1,and Ω∈L^q（S^n-1） for some q 〉 1/（1 -β）, then for any p∈（1, ∞）, and some appropriate 0 〈β〈 1, TA1,A2,...,Ar, is bounded on L^P（R^n）.
文摘We obtain appropriate sharp bounds on Triebel-Lizorkin spaces for rough oscillatory inte- grals with polynomial phase. By using these bounds and using an extrapolation argument we obtain some new and previously known results for oscillatory integrals under very weak size conditions on the kernel functions.
基金Supported by the National Natural Science Foundation of China (Grant No. 11071250)
文摘In this paper,the boundedness is obtained on the Triebel-Lizorkin spaces and the Besov spaces for a class of oscillatory singular integrals with Hardy kernels.
基金This author is partially supported by the National Science Foundation of ChinaZhejiang Provincial Sciences Foundation of China
文摘The boundedness on weighted local Hardy spaces h<sup>1,p</sup><sub>w</sub> of the oscillatory singular integral Tf（x）=∫<sub>R</sub><sup>n</sup> e<sup>iQ（x,y）</sup>K（x,y）f（y）dy is considered when Q（x,y）=P（x-y）for some real-valued polynomial P with its degree not less than two.Also a sufficient and necessary condition on polynomial Q on R<sup>n</sup> × R<sup>n</sup> such that T maps h<sup>1,p</sup><sub>w</sub> to the weighted integrable function space L<sup>1</sup><sub>w</sub> is found.
基金the National Natural Sciences Foundation of China (No.19131080) and the SEDF of China.
文摘In this paper, the authors prove that some oscillatory singular integral operators of non-convolution type with non-polynomial phases are bounded from the Herz-type Hardy spaces to the Herz spaces and from the Hardy spaces associated with the Beurling algebras to the Beurling algebras in higher dimensions, even though it is well-known that these operators are not bounded from the Hardy space H1(Rn) into the Lebesgue spaceL1(Rn).
基金Supported in part by National Natural Foundation of China (Grant No. 11071250)
文摘In this paper, we obtain the boundedness of the parabolic singular integral operator T with kernel in L（log L） 1/γ,（Sn- 1 ） on Triebel-Lizorkin spaces. Moreover, we prove the boundedness of a class of Marcinkiewicz integrals μΩ,q （f） from ｜｜f｜｜Fp^oq（Rn） into Lp （Rn）.
文摘Let h, be a measurable function defined on R^＋ ×R^＋. Let Ω ∈ L（log L^＋）^υq （S^n1-1 × S^n2-1） （1≤ υq ≤ 2） be homogeneous of degree zero and satisfy certain cancellation conditions. We show that the singular integral Tf（x1,x2）=p.v.∫∫R^n1＋n2 Ω（y′1,y′2）h（｜y1｜,｜y2｜）/｜y1｜^n1｜y2｜^n2 f（x1-y1,x2-y2）dy1dy2maps from Sp,q^α1,α2F（R^n1×R^n2）boundedly to itself for 1 〈 p, q 〈 ∞, α1, α2 ∈R.
文摘In this paper, the authors establish the weighted (L^p, L^q) estimates for aclass of multilinear oscillatory singular integrals with smooth phases. Certain endpoint estimatesare also considered.
基金Supported by the National Science Foundation of China (Grants 10901043, 10701064, 10871173, and 10931001)Hangdian Foundation (KYS075608076)
文摘In this paper, we prove the Triebel-Lizorkin boundedness for the Marcinkiewicz integral with rough kernel. The method we apply here enables us to consider more general operators.
基金Supported by the National Natural Science Foundation of China(12071437,12101562)the Natural Science Foundation of Zhejiang(LQ20A010003)the Natural Science Foundation from the Education Department of Anhui Province(KJ2017A847).
文摘In this article,we study the boundedness properties of the averaging operator S_(t)^(γ) on Triebel-Lizorkin spaces F_(p,q)^(α)(R^(n))for various p,q.As an application,we obtain the norm convergence rate for S_(t)^(γ)(f)on Triebel-Lizorkin spaces and the relation between the smoothness imposed on functions and the rate of norm convergence of S_(t)^(γ) is given.
基金Supported by National Natural Science Foundation of China （Grant No. 11071250） NWNU-KJCXGC-3-47 The authors would like to express their deep thanks to the referee for his/her very careful reading and many valuable comments and suggestions
文摘In this paper, the authors give the boundedness on Triebel-Lizorkin spaces for the parabolic singular integral with rough kernel and its commutator.
基金supported by the Program for New Century Excellent Talents in Fujian Province, National Natural Science Foundation of China (Grant No. 10601040)Tian Yuan Foundation of China(Grant No. 10526033)China Postdoctoral Science Foundation (Grant No. 2005038639)
文摘In this paper, we consider the rough singular integral operators on product Triebel-Lizorkin spaces and prove certain boundedness properties on the Triebel-Lizorkin spaces. We also use the same method to study the fractional integral operator and the Littlewood-Paley functions. The results extend some known results.
基金supported by the NSF of USA(Grant No.DMS0901761)supported by NNSF of China(Grant Nos.10971228and11271209)Natural Science Foundation of Nantong University(Grant No.11ZY002)
文摘Though the theory of Triebel-Lizorkin and Besov spaces in one-parameter has been developed satisfactorily, not so much has been done for the multiparameter counterpart of such a theory. In this paper, we introduce the weighted Triebel-Lizorkin and Besov spaces with an arbitrary number of parameters and prove the boundedness of singular integral operators on these spaces using discrete Littlewood-Paley theory and Calderon＇s identity. This is inspired by the work of discrete Littlewood- Paley analysis with two parameters of implicit dilations associated with the flag singular integrals recently developed by Han and Lu [12]. Our approach of derivation of the boundedness of singular integrals on these spaces is substantially different from those used in the literature where atomic decomposition on the one-parameter Triebel-Lizorkin and Besov spaces played a crucial role. The discrete Littlewood-Paley analysis allows us to avoid using the atomic decomposition or deep Journe＇s covering lemma in multiparameter setting.
基金supported partly by NSF of China (No. 10571015)SRFDP of China (No. 20050027025)+2 种基金supported by the U.S. NSF (Grant DMS No. 0500853)supported partly by NSF of China (No. 10771054)supported by NSF of China (No, 10811120558)
文摘Though the theory of one-parameter Triebel-Lizorkin and Besov spaces has been very well developed in the past decades, the multi-parameter counterpart of such a theory is still absent. The main purpose of this paper is to develop a theory of multi-parameter Triebel-Lizorkin and Besov spaces using the discrete Littlewood-Paley-Stein analysis in the setting of implicit multi-parameter structure. It is motivated by the recent work of Han and Lu in which they established a satisfactory theory of multi-parameter Littlewood-Paley-Stein analysis and Hardy spaces associated with the flag singular integral operators studied by Muller-Ricci-Stein and Nagel-Ricci-Stein. We also prove the boundedness of flag singular integral operators on Triebel-Lizorkin space and Besov space. Our methods here can be applied to develop easily the theory of multi-parameter Triebel-Lizorkin and Besov spaces in the pure product setting.
