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Boundedness Estimates for Commutators of Riesz Transforms Related to Schrödinger Operators 与Schrödinger算子相关的Riesz变换换向子的有界性估计
IF 0.6
Analysis in Theory and Applications Pub Date : 2018-06-01 DOI: 10.4208/ATA.OA-2017-0071
Y. He
{"title":"Boundedness Estimates for Commutators of Riesz Transforms Related to Schrödinger Operators","authors":"Y. He","doi":"10.4208/ATA.OA-2017-0071","DOIUrl":"https://doi.org/10.4208/ATA.OA-2017-0071","url":null,"abstract":"Let L=−∆+V be a Schrödinger operator on Rn(n≥ 3), where the nonnegative potential V belongs to reverse Hölder class RHq1 for q1 > n 2 . Let H p L(R n) be the Hardy space associated with L. In this paper, we consider the commutator [b,Tα], which associated with the Riesz transform Tα =Vα(−∆+V)−α with 0< α≤ 1, and a locally integrable function b belongs to the new Campanato space Λβ(ρ). We establish the boundedness of [b,Tα] from Lp(Rn) to Lq(Rn) for 1 < p < q1/α with 1/q= 1/p−β/n. We also show that [b,Tα] is bounded from H L(R n) to Lq(Rn) when n/(n+β)< p≤ 1,1/q = 1/p−β/n. Moreover, we prove that [b,Tα] maps H n n+β L (R n) continuously into weak L1(Rn).","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"23 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84189346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hopf Bifurcation of a Nonresident Computer Virus Model with Delay 一类具有时滞的非驻留计算机病毒模型的Hopf分岔
IF 0.6
Analysis in Theory and Applications Pub Date : 2018-06-01 DOI: 10.4208/ata.oa-2016-0035
Zizhen Zhang
{"title":"Hopf Bifurcation of a Nonresident Computer Virus Model with Delay","authors":"Zizhen Zhang","doi":"10.4208/ata.oa-2016-0035","DOIUrl":"https://doi.org/10.4208/ata.oa-2016-0035","url":null,"abstract":"","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"34 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83114675","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Commutators of Singular Integral Operators Related to Magnetic Schrödinger Operators 与磁算子相关的奇异积分算子的换易子Schrödinger算子
IF 0.6
Analysis in Theory and Applications Pub Date : 2018-06-01 DOI: 10.4208/ATA.2018.V34.N1.4
Wanqing Liu
{"title":"Commutators of Singular Integral Operators Related to Magnetic Schrödinger Operators","authors":"Wanqing Liu","doi":"10.4208/ATA.2018.V34.N1.4","DOIUrl":"https://doi.org/10.4208/ATA.2018.V34.N1.4","url":null,"abstract":"Let A:=−(∇−i~a)·(∇−i~a)+V be a magnetic Schrödinger operator on L2(Rn), n ≥ 2, where ~a := (a1,··· ,an) ∈ Lloc(R,R) and 0 ≤ V ∈ Lloc(R). In this paper, we show that for a function b in Lipschitz space Lipα(R n) with α∈ (0,1), the commutator [b,V1/2 A−1/2] is bounded from Lp(Rn) to Lq(Rn), where p,q∈ (1,2] and 1/p−1/q= α/n.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"7 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77052924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Smulyan Lemma and Differentiability of the Support Function 支持函数的Smulyan引理与可微性
IF 0.6
Analysis in Theory and Applications Pub Date : 2018-06-01 DOI: 10.4208/ata.oa-2017-0024
Ildar Sadeqi and Sima Hassankhali
{"title":"Smulyan Lemma and Differentiability of the Support Function","authors":"Ildar Sadeqi and Sima Hassankhali","doi":"10.4208/ata.oa-2017-0024","DOIUrl":"https://doi.org/10.4208/ata.oa-2017-0024","url":null,"abstract":"The purpose of this paper is to verify the Smulyan lemma for the support function, and also the Gateaux differentiability of the support function is studied on its domain. Moreover, we provide a characterization of Frechet differentiability of the support function on the extremal points.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"124 1","pages":"348-357"},"PeriodicalIF":0.6,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87886190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Approximation for Certain Stancu Type Summation Integral Operator 一类姿态型求和积分算子的近似
IF 0.6
Analysis in Theory and Applications Pub Date : 2018-06-01 DOI: 10.4208/ATA.2018.V34.N1.6
P. Maheshwari
{"title":"Approximation for Certain Stancu Type Summation Integral Operator","authors":"P. Maheshwari","doi":"10.4208/ATA.2018.V34.N1.6","DOIUrl":"https://doi.org/10.4208/ATA.2018.V34.N1.6","url":null,"abstract":"In the present paper, we consider Stancu type generalization of the summation integral type operators discussed in [15]. We apply hypergeometric series for obtaining moments of these operators. We also discuss about asymptotic formula and error estimation in terms of modules of continuity.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"13 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73185477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Generalized Inverse Analysis on the Domain Ω(A,A +) in B(E,F) B(E,F)中Ω(A,A +)域的广义逆分析
IF 0.6
Analysis in Theory and Applications Pub Date : 2018-06-01 DOI: 10.4208/ATA.2018.V34.N2.3
Zhaofeng Ma
{"title":"Generalized Inverse Analysis on the Domain Ω(A,A +) in B(E,F)","authors":"Zhaofeng Ma","doi":"10.4208/ATA.2018.V34.N2.3","DOIUrl":"https://doi.org/10.4208/ATA.2018.V34.N2.3","url":null,"abstract":"","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"45 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80252103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Weighted Lp-Approximation by Weighted Bernstein-Durrmeyer Operators 加权Bernstein-Durrmeyer算子的加权lp逼近
IF 0.6
Analysis in Theory and Applications Pub Date : 2018-06-01 DOI: 10.4208/ATA.2018.V34.N1.1
Meili Wang
{"title":"On Weighted Lp-Approximation by Weighted Bernstein-Durrmeyer Operators","authors":"Meili Wang","doi":"10.4208/ATA.2018.V34.N1.1","DOIUrl":"https://doi.org/10.4208/ATA.2018.V34.N1.1","url":null,"abstract":"Abstract. In the present paper, we establish direct and converse theorems for weighted Bernstein-Durrmeyer operators under weighted Lp−norm with Jacobi weight w(x) = xα(1−x). All the results involved have no restriction α,β< 1− p , which indicates that the weighted Bernstein-Durrmeyer operators have some better approximation properties than the usual Bernstein-Durrmeyer operators.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"24 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82984666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some Estimates for the Fourier Transform on Rank 1 Symmetric Space 秩1对称空间上傅里叶变换的一些估计
IF 0.6
Analysis in Theory and Applications Pub Date : 2018-06-01 DOI: 10.4208/ata.2018.v34.n2.1
M. E. Hamma
{"title":"Some Estimates for the Fourier Transform on Rank 1 Symmetric Space","authors":"M. E. Hamma","doi":"10.4208/ata.2018.v34.n2.1","DOIUrl":"https://doi.org/10.4208/ata.2018.v34.n2.1","url":null,"abstract":"","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"275 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77097826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Characterization of Nonuniform Tight Wavelet Frames on Local Fields 局部域上非均匀紧小波帧的表征
IF 0.6
Analysis in Theory and Applications Pub Date : 2018-06-01 DOI: 10.4208/ATA.2018.V34.N2.4
Owais Ahmad and Neyaz A. Sheikh
{"title":"On Characterization of Nonuniform Tight Wavelet Frames on Local Fields","authors":"Owais Ahmad and Neyaz A. Sheikh","doi":"10.4208/ATA.2018.V34.N2.4","DOIUrl":"https://doi.org/10.4208/ATA.2018.V34.N2.4","url":null,"abstract":"In this article, we introduce a notion of nonuniform wavelet frames on local fields of positive characteristic. Furthermore, we gave a complete characterization of tight nonuniform wavelet frames on local fields of positive characteristic via Fourier transform. Our results also hold for the Cantor dyadic group and the Vilenkin groups as they are local fields of positive characteristic.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"11 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83973217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 19
Harmonic Polynomials Via Differentiation 微分求调和多项式
IF 0.6
Analysis in Theory and Applications Pub Date : 2018-06-01 DOI: 10.4208/ata.oa-2017-0062
R. Estrada
{"title":"Harmonic Polynomials Via Differentiation","authors":"R. Estrada","doi":"10.4208/ata.oa-2017-0062","DOIUrl":"https://doi.org/10.4208/ata.oa-2017-0062","url":null,"abstract":"It is well-known that if p is a homogeneous polynomial of degree k in n variables, p∈Pk, then the ordinary derivative p(∇) ( r2−n ) has the form An,kY(x)r where An,k is a constant and where Y is a harmonic homogeneous polynomial of degree k, Y∈Hk, actually the projection of p onto Hk. Here we study the distributional derivative p ( ∇ )( r2−n ) and show that the ordinary part is still a multiple of Y, but that the delta part is independent of Y, that is, it depends only on p−Y. We also show that the exponent 2−n is special in the sense that the corresponding results for p(∇)(rα) do not hold if α 6=2−n. Furthermore, we establish that harmonic polynomials appear as multiples of r2−n−2k−2k ′ when p(∇) is applied to harmonic multipoles of the form Y′ (x)r2−n−2k for some Y∈Hk.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"13 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87089076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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