The Effect of the Smoothness of Fractional Type Operators Over Their Commutators with Lipschitz Symbols on Weighted Spaces

被引：0
作者：
Dalmasso Estefanía
Gladis Pradolini
Wilfredo Ramos
机构：
[1] UNL,Instituto de Matemática Aplicada del Litoral
[2] CONICET,Facultad de Ingeniería Química
[3] FIQ Predio Dr. Alberto Cassano del CCT-CONICET-Santa Fe,Facultad de Ciencias Exactas y Naturales y Agrimensura
[4] UNL,undefined
[5] UNNE,undefined
来源：
Fractional Calculus and Applied Analysis | 2018年 / 21卷
关键词：
Primary 42B25; Secondary 42B35; fractional calculus operators; commutators; Lipschitz symbols; weights;
D O I：
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中图分类号：
学科分类号：
摘要：
We prove boundedness results for integral operators of fractional type and their higher order commutators between weighted spaces, including L2-Lq, Lq-BMO and L2-Lipschitz estimates. The kernels of such operators satisfy certain size condition and a Lipschitz type regularity, and the symbol of the commutator belongs to a Lipschitz class. We also deal with commutators of fractional type operators with less regular kernels satisfying a Hörmander’s type inequality. As far as we know, these last results are new even in the unweighted case. Moreover, we give a characterization result involving symbols of the commutators and continuity results for extreme values of p.
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页码：628 / 653
页数：25
相关论文
共 77 条
[1]  
Bernardis A(2014)Generalized maximal functions and related operators on weighted Musielak-Orlicz spaces Ann. Acad. Sci. Fenn. Math. 39 23-50
[2]  
Dalmasso E(2006)Weighted inequalities for commutators of fractional integrals on spaces of homogeneous type J. Math. Anal. Appl. 322 825-846
[3]  
Pradolini G(2011)Weighted inequalities for fractional integral operators with kernel satisfying Hörmander type conditions Math. Inequal. Appl. 14 881-895
[4]  
Bernardis A(1996) estimates for some ultraparabolic operators with discontinuous coefficients J. Math. Anal. Appl. 200 332-354
[5]  
Hartzstein S(1982)A note on commutators Indiana Univ. Math. J. 31 7-16
[6]  
Pradolini G(1993)Some integral and maximal operators related to starlike sets Studia Math. 107 223-255
[7]  
Bernardis AL(1991)Interior Ricerche Mat. 40 149-168
[8]  
Lorente M(1993) estimates for nondivergence elliptic equations with discontinuous coefficients Trans. Amer. Math. Soc. 336 841-853
[9]  
Riveros MS(2003)-solvability of the Dirichlet problem for nondivergence elliptic equations with VMO coefficients Publ. Mat. 47 103-131
[10]  
Bramanti M(2017)Endpoint estimates and weighted norm inequalities for commutators of fractional integrals Math. Nach. 290 19-36
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