The present paper introduces a kind of Nevai-Durrmeyer operators which can be used to approximate functions in Lω^p, spaces with the weight ω(x)=1/√(1-x^2) and the approximate rate is also estimated.
Let G be a locally compact unimodular group with Haar measure rmdx and ω be the Beurling's weight function on G (Reiter, [10]). In this paper the authors define a space Aωp,q (G) and prove that Aωp,q (G) is a t...Let G be a locally compact unimodular group with Haar measure rmdx and ω be the Beurling's weight function on G (Reiter, [10]). In this paper the authors define a space Aωp,q (G) and prove that Aωp,q (G) is a translation invariant Banach space. Fur- thermore the authors discuss inclusion properties and show that if G is a locally compact abelian group then Aωp,q (G) admits an approximate identity bounded in Lω1 (G). It is also proved that the space Lωp (G) Lω1 Lωq (G) is isometrically isomorphic to the space Aωp,q (G) and the space of multipliers from Lωp (G) to Lq-1, (G) is isometrically isomorphic to the dual of the space Aωp,q (G) iff G satisfies a property Ppq. At the end of this work it is showed that if G is a locally compact abelian group then the space of all multipliers from Lω1 (G) to Aωp,q (G) is the space Aωp,q (G).展开更多
We give some properties of the composition and multiplication operators on L^(p,∞)(M), where M is a semifinite von Neumann algebra with a normal semifinite faithful trace τ.
In this paper, some weighted estimates for the multivariate Hausdorff operators are obtained. It is proved that the multivariate Hausdorff operators are bounded on LP spaces with power weights, which is based on the b...In this paper, some weighted estimates for the multivariate Hausdorff operators are obtained. It is proved that the multivariate Hausdorff operators are bounded on LP spaces with power weights, which is based on the boundedness of multivariate Hausdorff operators on Herz spaces, and are bounded on weighted LP spaces with the weights satisfying the homogeneity of degree zero.展开更多
In this paper we study the problem of characterizing the real Banach spaces whose unit sphere determines polynomials, i.e., if two polynomials coincide in the unit sphere, is this sufficient to guarantee that they are...In this paper we study the problem of characterizing the real Banach spaces whose unit sphere determines polynomials, i.e., if two polynomials coincide in the unit sphere, is this sufficient to guarantee that they are identical? We show that, in the frame of spaces with unconditional basis, non- reflexivity is a sufficient, although not necessary, condition for the above question to have an affirmative answer. We prove that the only lp^n spaces having this property are those with p irrational, while the only lp spaces which do not enjoy it are those with p an even integer. We also introduce a class of polynomial determining sets in any real Banach space.展开更多
We investigate Besov spaces and their connection with trigonometric polynomial approximation in L_p[-π,π], algebraic polynomial approximation in L_p[-1,1], algebraic polynomial approximation in L_p(S), and entir...We investigate Besov spaces and their connection with trigonometric polynomial approximation in L_p[-π,π], algebraic polynomial approximation in L_p[-1,1], algebraic polynomial approximation in L_p(S), and entire function of exponential type approximation in Lp(R), and characterize K-functionals for certain pairs of function spaces including (Lp [-π,π], B_s~α (Lp[-π,π])), (L_p(R),B_s~α (Lp(R))), (Lp[-1,1],B_s~α (Lp[-1,1])), and (Lp(S),B_s~α (Lp(S))), where 0<s<, 0<p<1, S is a simple polytope and 0<α<r.展开更多
In this paper, we treat a class of non-standard commutators with higher order remainders in the Lipschitz spaces and give (L^v, L^q), (H^p, L^q) boundedness and the boundedness in the Triebel- Lizorkin spaces. Our...In this paper, we treat a class of non-standard commutators with higher order remainders in the Lipschitz spaces and give (L^v, L^q), (H^p, L^q) boundedness and the boundedness in the Triebel- Lizorkin spaces. Our results give simplified proofs of the recent works by Chen, and extend his result.展开更多
In this paper, we continue studying the so-called non-linear best m-term one-sided approximation problems and obtain the asymptotic estimations of non-linear best m-term one-sided trigonometric approximation under the...In this paper, we continue studying the so-called non-linear best m-term one-sided approximation problems and obtain the asymptotic estimations of non-linear best m-term one-sided trigonometric approximation under the norm Lp (1 ≤ p ≤ ∞) of multiplier function classes and the corresponding m-term Greedy-liked one-sided trigonometric approximation results.展开更多
The mixed principal eigenvalue of p-Laplacian (equivalently, the optimal constant of weighted Hardy inequality in Lp space) is studied in this paper. Several variational formulas for the eigenvalue are presented. As...The mixed principal eigenvalue of p-Laplacian (equivalently, the optimal constant of weighted Hardy inequality in Lp space) is studied in this paper. Several variational formulas for the eigenvalue are presented. As applications of the formulas, a criterion for the positivity of the eigenvalue is obtained. Furthermore, an approximating procedure and some explicit estimates are presented case by case. An example is included to illustrate the power of the results of the paper.展开更多
In the recent work, we have developed a decay framework in general Lp critical spaces and established optimal time-decay estimates for barotropic compressible Navier-Stokes equations. Those decay rates of Lq-Lr type o...In the recent work, we have developed a decay framework in general Lp critical spaces and established optimal time-decay estimates for barotropic compressible Navier-Stokes equations. Those decay rates of Lq-Lr type of the solution and its derivatives are available in the critical regularity framework, which were exactly firstly observed by Matsumura & Nishida, and subsequently generalized by Ponce for solutions with high Sobolev regularity. We would like to mention that our approach is likely to be effective for other hyperbolic/parabolic systems that are encountered in fluid mechanics or mathematical physics. In this paper, a new observation is involved in the high frequency, which enables us to improve decay exponents for the high frequencies of solutions.展开更多
基金Supported by Scientific Research Fund of Zhejiang Provincial Education Department(No. 20030431)the Young College Teachers Program of Zhejiang Province, and the Young Doctor Foundation of City of Ningbo (No. 2004A620017, 2005A620032).
文摘The present paper introduces a kind of Nevai-Durrmeyer operators which can be used to approximate functions in Lω^p, spaces with the weight ω(x)=1/√(1-x^2) and the approximate rate is also estimated.
文摘Let G be a locally compact unimodular group with Haar measure rmdx and ω be the Beurling's weight function on G (Reiter, [10]). In this paper the authors define a space Aωp,q (G) and prove that Aωp,q (G) is a translation invariant Banach space. Fur- thermore the authors discuss inclusion properties and show that if G is a locally compact abelian group then Aωp,q (G) admits an approximate identity bounded in Lω1 (G). It is also proved that the space Lωp (G) Lω1 Lωq (G) is isometrically isomorphic to the space Aωp,q (G) and the space of multipliers from Lωp (G) to Lq-1, (G) is isometrically isomorphic to the dual of the space Aωp,q (G) iff G satisfies a property Ppq. At the end of this work it is showed that if G is a locally compact abelian group then the space of all multipliers from Lω1 (G) to Aωp,q (G) is the space Aωp,q (G).
基金Supported by the National Natural Science Foundation of China(11371304,11401507)
文摘We give some properties of the composition and multiplication operators on L^(p,∞)(M), where M is a semifinite von Neumann algebra with a normal semifinite faithful trace τ.
文摘In this paper, some weighted estimates for the multivariate Hausdorff operators are obtained. It is proved that the multivariate Hausdorff operators are bounded on LP spaces with power weights, which is based on the boundedness of multivariate Hausdorff operators on Herz spaces, and are bounded on weighted LP spaces with the weights satisfying the homogeneity of degree zero.
文摘In this paper we study the problem of characterizing the real Banach spaces whose unit sphere determines polynomials, i.e., if two polynomials coincide in the unit sphere, is this sufficient to guarantee that they are identical? We show that, in the frame of spaces with unconditional basis, non- reflexivity is a sufficient, although not necessary, condition for the above question to have an affirmative answer. We prove that the only lp^n spaces having this property are those with p irrational, while the only lp spaces which do not enjoy it are those with p an even integer. We also introduce a class of polynomial determining sets in any real Banach space.
基金This project is supported by the National Natural Science Foundation of China.
文摘We investigate Besov spaces and their connection with trigonometric polynomial approximation in L_p[-π,π], algebraic polynomial approximation in L_p[-1,1], algebraic polynomial approximation in L_p(S), and entire function of exponential type approximation in Lp(R), and characterize K-functionals for certain pairs of function spaces including (Lp [-π,π], B_s~α (Lp[-π,π])), (L_p(R),B_s~α (Lp(R))), (Lp[-1,1],B_s~α (Lp[-1,1])), and (Lp(S),B_s~α (Lp(S))), where 0<s<, 0<p<1, S is a simple polytope and 0<α<r.
基金Supported by RFDP of China (Grant No. 20050027025)NSF of China (Grant No. 10571014, 10571015)
文摘In this paper, we treat a class of non-standard commutators with higher order remainders in the Lipschitz spaces and give (L^v, L^q), (H^p, L^q) boundedness and the boundedness in the Triebel- Lizorkin spaces. Our results give simplified proofs of the recent works by Chen, and extend his result.
基金Supported by National Natural Science Foundation of China (Grant No. 10771016) supported by Shandong Agricultural University Youth Foundation
文摘In this paper, we continue studying the so-called non-linear best m-term one-sided approximation problems and obtain the asymptotic estimations of non-linear best m-term one-sided trigonometric approximation under the norm Lp (1 ≤ p ≤ ∞) of multiplier function classes and the corresponding m-term Greedy-liked one-sided trigonometric approximation results.
基金Acknowledgements The authors would like to thank Professor Yonghua Mao for his helpful comments and suggestions. This work was supported in part by the National Natural Science Foundation of China (Grant No. 11131003), the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20100003110005), the '985' project from the Ministry of Education in China, and the Fundamental Research Funds for the Central Universities.
文摘The mixed principal eigenvalue of p-Laplacian (equivalently, the optimal constant of weighted Hardy inequality in Lp space) is studied in this paper. Several variational formulas for the eigenvalue are presented. As applications of the formulas, a criterion for the positivity of the eigenvalue is obtained. Furthermore, an approximating procedure and some explicit estimates are presented case by case. An example is included to illustrate the power of the results of the paper.
基金Supported by the National Natural Science Foundation of China(Grant No.11471158)the Program for New Century Excellent Talents in University(Grant No.NCET-13–0857)the Fundamental Research Funds for the Central Universities(Grant No.NE2015005)
文摘In the recent work, we have developed a decay framework in general Lp critical spaces and established optimal time-decay estimates for barotropic compressible Navier-Stokes equations. Those decay rates of Lq-Lr type of the solution and its derivatives are available in the critical regularity framework, which were exactly firstly observed by Matsumura & Nishida, and subsequently generalized by Ponce for solutions with high Sobolev regularity. We would like to mention that our approach is likely to be effective for other hyperbolic/parabolic systems that are encountered in fluid mechanics or mathematical physics. In this paper, a new observation is involved in the high frequency, which enables us to improve decay exponents for the high frequencies of solutions.