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Inhomogeneous Besov and Triebel-Lizorkin spaces associated with a para-accretive function and their applications
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作者 LIAO Fang-hui LIU Zong-guang ZHANG Xiao-jin 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第4期493-509,共17页
In this paper,using inhomogeneous Calderon’s reproducing formulas and the space of test functions associated with a para-accretive function,the inhomogeneous Besov and TriebelLizorkin spaces are established.As applic... In this paper,using inhomogeneous Calderon’s reproducing formulas and the space of test functions associated with a para-accretive function,the inhomogeneous Besov and TriebelLizorkin spaces are established.As applications,pointwise multiplier theorems are also obtained. 展开更多
关键词 para-accretive function Calderon's reproducing formula Besov space triebel-lizorkin space pointwise multiplier
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CHARACTERIZATION OF MULTIPLIER SPACES WITH DAUBECHIES WAVELETS 被引量:2
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作者 杨奇祥 《Acta Mathematica Scientia》 SCIE CSCD 2012年第6期2315-2321,共7页
We characterize the multiplier spaces from Sobolev spaces to L2 with Daubechles wavelets without using capacity.
关键词 Daubechies wavelet multiplier spaces Morrey spaces
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WAVELET CHARACTERIZATION OF WEIGHTED TRIEBEL-LIZORKIN SPACES 被引量:1
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作者 Deng Donggao Xu Ming Yan Lixin (Zhongshan University, China) 《Approximation Theory and Its Applications》 2002年第4期76-92,共17页
In this paper we use wavelets to characterize weighted Triebel-Lizorkin spaces. Our weights belong to the Muckenhoupt class A q and our weighted Triebel-Lizorkin spaces are weighted atomic Triebel-Lizorkin spaces.
关键词 wavelet CHARACTERIZATION OF WEIGHTED triebel-lizorkin spaces
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Performance evaluation of wavelet scattering network in image texture classification in various color spaces 被引量:2
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作者 伍家松 姜龙玉 +2 位作者 韩旭 Lotfi Senhadji 舒华忠 《Journal of Southeast University(English Edition)》 EI CAS 2015年第1期46-50,共5页
The optimized color space is searched by using the wavelet scattering network in the KTH_TIPS_COL color image database for image texture classification. The effect of choosing the color space on the classification acc... The optimized color space is searched by using the wavelet scattering network in the KTH_TIPS_COL color image database for image texture classification. The effect of choosing the color space on the classification accuracy is investigated by converting red green blue (RGB) color space to various other color spaces. The results show that the classification performance generally changes to a large degree when performing color texture classification in various color spaces, and the opponent RGB-based wavelet scattering network outperforms other color spaces-based wavelet scattering networks. Considering that color spaces can be changed into each other, therefore, when dealing with the problem of color texture classification, converting other color spaces to the opponent RGB color space is recommended before performing the wavelet scattering network. 展开更多
关键词 wavelet scattering network color texture classification color spaces opponent mechanism
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APPLICATIONS OF HERZ-TYPE TRIEBEL-LIZORKIN SPACES 被引量:11
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作者 徐景实 杨大春 《Acta Mathematica Scientia》 SCIE CSCD 2003年第3期328-338,共11页
In this paper, the authors first establish the connections between the Herz-type Triebel-Lizorkin spaces and the well-known Herz-type spaces; the authors then study the pointwise multipliers for the Herz-type Triebel-... In this paper, the authors first establish the connections between the Herz-type Triebel-Lizorkin spaces and the well-known Herz-type spaces; the authors then study the pointwise multipliers for the Herz-type Triebel-Lizorkin spaces and show that pseudo-differential operators are bounded on these spaces by using pointwise multipliers. 展开更多
关键词 Herz-type space triebel-lizorkin space pointwise multiplier pseudodifferential operator maximal operator
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A CHARACTERIZATION OF ORTHONORMAL WAVELET FAMILIES IN SOBOLEV SPACES 被引量:6
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作者 鲁大勇 李登峰 《Acta Mathematica Scientia》 SCIE CSCD 2011年第4期1475-1488,共14页
In this paper, a characterization of orthonormal wavelet families in Sobolev spaces H s (R) is established.
关键词 wavelets orthonormal wavelet families Sobolev spaces
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A DISCRETE CHARACTERIZATION OF HERZ-TYPE TRIEBEL-LIZORKIN SPACES AND ITS APPLICATIONS 被引量:8
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作者 XuJingshi 《Acta Mathematica Scientia》 SCIE CSCD 2004年第3期412-420,共9页
In this paper, the author establishes a discrete characterization of the Herz-type Triebel-Lizorkin spaces which is used to prove the boundedness of pseudo-differential operators on these function spaces.
关键词 Herz-type space triebel-lizorkin space discrete characterization pseudo-differential operator maximal operator
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Function spaces of Besov-type and Triebel-Lizorkin-type——a survey 被引量:3
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作者 YANG Da-chun YUAN Wen 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2013年第4期405-426,共22页
This article is devoted to presenting a recapitulative introduction for the theory of Besov-type and Triebel-Lizorkin-type spaces developed in recent years.
关键词 Besov space triebel-lizorkin space EMBEDDING ATOM MOLECULE wavelet local mean Peetre maximal function dual complex interpolation
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Strategies for multi-step-ahead available parking spaces forecasting based on wavelet transform 被引量:4
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作者 JI Yan-jie GAO Liang-peng +1 位作者 CHEN Xiao-shi GUO Wei-hong 《Journal of Central South University》 SCIE EI CAS CSCD 2017年第6期1503-1512,共10页
A new methodology for multi-step-ahead forecasting was proposed herein which combined the wavelet transform(WT), artificial neural network(ANN) and forecasting strategies based on the changing characteristics of avail... A new methodology for multi-step-ahead forecasting was proposed herein which combined the wavelet transform(WT), artificial neural network(ANN) and forecasting strategies based on the changing characteristics of available parking spaces(APS). First, several APS time series were decomposed and reconstituted by the wavelet transform. Then, using an artificial neural network, the following five strategies for multi-step-ahead time series forecasting were used to forecast the reconstructed time series: recursive strategy, direct strategy, multi-input multi-output(MIMO) strategy, DIRMO strategy(a combination of the direct and MIMO strategies), and newly proposed recursive multi-input multi-output(RECMO) strategy which is a combination of the recursive and MIMO strategies. Finally, integrating the predicted results with the reconstructed time series produced the final forecasted available parking spaces. Three findings appear to be consistently supported by the experimental results. First, applying the wavelet transform to multi-step ahead available parking spaces forecasting can effectively improve the forecasting accuracy. Second, the forecasting resulted from the DIRMO and RECMO strategies is more accurate than that of the other strategies. Finally, the RECMO strategy requires less model training time than the DIRMO strategy and consumes the least amount of training time among five forecasting strategies. 展开更多
关键词 available PARKING spaces MULTI-STEP AHEAD time series forecasting wavelet transform forecasting STRATEGIES recursive multi-input MULTI-OUTPUT strategy
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Boundedness of Marcinkiewicz integral on Triebel-Lizorkin spaces 被引量:5
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作者 ZHANG Chun-jie CHEN Jie-cheng 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2010年第1期48-54,共7页
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.
关键词 Marcinkiewicz integral triebel-lizorkin spaces rough kernel singular integral.
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THE BOUNDEDNESS OF MULTILINEAR COMMUTATORS FROM L^p(R^n) TO TRIEBEL-LIZORKIN SPACES 被引量:4
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作者 Yanping Chen Bolin Ma 《Analysis in Theory and Applications》 2007年第2期112-128,共17页
Let b^→=(b1,…,bm),bi∈∧°βi(R^n),1≤i≤m,0〈βi〈β,0〈β〈1,[B^→,T]f(x)=∫R^n(b1(x)-b1(y))…(bm(x)-bm(y))K(x-y)f(y)dy,where K is a Calder6n-Zygmund kernel. In this paper, we show that ... Let b^→=(b1,…,bm),bi∈∧°βi(R^n),1≤i≤m,0〈βi〈β,0〈β〈1,[B^→,T]f(x)=∫R^n(b1(x)-b1(y))…(bm(x)-bm(y))K(x-y)f(y)dy,where K is a Calder6n-Zygmund kernel. In this paper, we show that [b^→,T] is bounded from L^p(R^n) to Fp^β,∞(R^n),as well as [b^→,1α]form L^p (R^n) to Fp^β,∞(R^n),where 1/q=1/p-α/n. 展开更多
关键词 multilinear commutator Calderon-Zygmund kernel Lipschitz space triebel-lizorkin space
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DUALITY OF WEIGHTED MULTIPARAMETER TRIEBEL-LIZORKIN SPACES 被引量:2
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作者 丁卫 朱月萍 《Acta Mathematica Scientia》 SCIE CSCD 2017年第4期1083-1104,共22页
In this paper, we reintroduce the weighted multi-parameter Triebel-Lizorkin spaces Fp^a,q(w;R^n1×R^n2) based on the Frazier and Jawerth' method in [11]. This space was firstly introduced in [18]. Then we estab... In this paper, we reintroduce the weighted multi-parameter Triebel-Lizorkin spaces Fp^a,q(w;R^n1×R^n2) based on the Frazier and Jawerth' method in [11]. This space was firstly introduced in [18]. Then we establish its dual space and get that (Fp'q)* = CMOp^-a,q' for 0 ~p≤ 1. 展开更多
关键词 triebel-lizorkin space WEIGHTED MULTIPARAMETER DUALITY Fefferman-Stein inequality
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BOUNDEDNESS OF PARABOLIC SINGULAR INTEGRALS AND MARCINKIEWICZ INTEGRALS ON TRIEBEL-LIZORKIN SPACES 被引量:3
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作者 Yaoming Niu Shuangping Tao 《Analysis in Theory and Applications》 2011年第1期59-75,共17页
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
关键词 parabolic singular integral triebel-lizorkin space Marcinkiewica integral rough kernel
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A CLASS OF OSCILLATORY SINGULAR INTEGRALS ON TRIEBEL-LIZORKIN SPACES 被引量:3
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作者 Jiang Liya Chen Jiecheng 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2006年第1期69-78,共10页
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
关键词 oscillatory singular integral triebel-lizorkin space.
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Characterizations of realized homogeneous Besov and Triebel-Lizorkin spaces via differences 被引量:1
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作者 MOUSSAI Madani 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2018年第2期188-208,共21页
Based on the role of the polynomial functions on the homogeneous Besov spaces, on the homogeneous Triebel-Lizorkin spaces and on their realized versions, we study and obtain characterizations of these spaces via diffe... Based on the role of the polynomial functions on the homogeneous Besov spaces, on the homogeneous Triebel-Lizorkin spaces and on their realized versions, we study and obtain characterizations of these spaces via difference operators in a certain sense. 展开更多
关键词 homogeneous Besov space homogeneous triebel-lizorkin space Nikol'skij representation method REALIZATIONS Hardy estimates
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Methodology of Wavelets in Relativistic Heavy Ion Collisions in One Dimensional Phase Space (<i>η</i>-Space) 被引量:1
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作者 Vyacheslav V. Lyashenko M. Ayaz Ahmad +1 位作者 Zhanna V. Deineko Mir Hashim Rasool 《Journal of High Energy Physics, Gravitation and Cosmology》 2017年第2期254-266,共13页
An attempt has been made to apply the wavelet methodology for the study of the results of the chaotic behavior of multiparticle production in relativistic heavy ion collisions. We reviewed the data that describes the ... An attempt has been made to apply the wavelet methodology for the study of the results of the chaotic behavior of multiparticle production in relativistic heavy ion collisions. We reviewed the data that describes the collisions of relativistic heavy ion for the case η-space in 1-D phase space of variable. We compared the experimental data and UrQMD data using wavelet coherency. We discussed the results of the comparison. 展开更多
关键词 wavelet Coherence Morlet wavelet Heavy Ion Collisions Reaction Dynamics Phase space Normalized FACTORIAL MOMENTS
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THE BESOV AND TRIEBEL-LIZORKIN SPACES WITH HIGH ORDER ON THE LIPSCHITZ CURVES 被引量:1
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作者 D.G.Deng Y.S.Han 《Analysis in Theory and Applications》 1993年第4期89-106,共18页
The Besov spaces B_p^(α,4)(Γ)and Triebel-Lizorkin spaces F_p^(α,4)(Γ)with high order x∈R on a Lipschitz curve Γ are defind,when 1≤p≤∞,1≤q≤∞.To compare to the classical case.a difference characterization of... The Besov spaces B_p^(α,4)(Γ)and Triebel-Lizorkin spaces F_p^(α,4)(Γ)with high order x∈R on a Lipschitz curve Γ are defind,when 1≤p≤∞,1≤q≤∞.To compare to the classical case.a difference characterization of such spaces in the case|x|<1 is given also. 展开更多
关键词 THE BESOV AND triebel-lizorkin spaces WITH HIGH ORDER ON THE LIPSCHITZ CURVES SHOW
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Boundedness of Fractional Integrals with a Rough Kernel on the Product Triebel-Lizorkin Spaces
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作者 zhang hui-hui yu xiao +1 位作者 xiang zhong-qi ji you-qing 《Communications in Mathematical Research》 CSCD 2017年第3期259-273,共15页
By using the Littlewood-Paley decomposition and the interpolation theory, we prove the boundedness of fractional integral on the product Triebel-Lizorkin spaces with a rough kernel related to the product block spaces.
关键词 fractional integral block space triebel-lizorkin space product space
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A NOTE ON SINGULAR INTEGRALS WITH DOMINATING MIXED SMOOTHNESS IN TRIEBEL-LIZORKIN SPACES
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作者 Hung Viet LE 《Acta Mathematica Scientia》 SCIE CSCD 2014年第4期1331-1344,共14页
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
关键词 singular integrals Marcinkiewicz integrals mixed smoothness triebel-lizorkin spaces
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Boundedness of oscillatory singular integral with rough kernels on Triebel-Lizorkin spaces
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作者 ZHANG Chun-jie ZHANG Yan-dan 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2013年第1期90-100,共11页
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
关键词 Oscillatory singular integral triebel-lizorkin space rough kernel phase function.
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