Fractional and Singular Integrals in Grand Morrey Spaces

2016 ◽  
pp. 871-924
Author(s):  
Vakhtang Kokilashvili ◽  
Alexander Meskhi ◽  
Humberto Rafeiro ◽  
Stefan Samko
Keyword(s):  
Singular Integrals ◽  
Morrey Spaces

scholarly journals Variation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spaces

2021 ◽  
Vol 11 (1) ◽  
pp. 72-95
Author(s):  
Xiao Zhang ◽  
Feng Liu ◽  
Huiyun Zhang
Keyword(s):  
Hilbert Transform ◽  
Besov Spaces ◽  
Singular Integrals ◽  
Riesz Transform ◽  
Morrey Spaces ◽  
Riesz Transforms ◽  
Rough Kernels ◽  
Lebesgue Spaces ◽  
Variation Operators

Abstract This paper is devoted to investigating the boundedness, continuity and compactness for variation operators of singular integrals and their commutators on Morrey spaces and Besov spaces. More precisely, we establish the boundedness for the variation operators of singular integrals with rough kernels Ω ∈ Lq (S n−1) (q > 1) and their commutators on Morrey spaces as well as the compactness for the above commutators on Lebesgue spaces and Morrey spaces. In addition, we present a criterion on the boundedness and continuity for a class of variation operators of singular integrals and their commutators on Besov spaces. As applications, we obtain the boundedness and continuity for the variation operators of Hilbert transform, Hermit Riesz transform, Riesz transforms and rough singular integrals as well as their commutators on Besov spaces.

scholarly journals Precompact Sets, Boundedness, and Compactness of Commutators for Singular Integrals in Variable Morrey Spaces

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Wei Wang ◽  
Jingshi Xu
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Singular Integrals ◽  
Sufficient Conditions ◽  
Morrey Spaces ◽  
Bmo Function

We give sufficient conditions for subsets to be precompact sets in variable Morrey spaces. Then we obtain the boundedness of the commutator generated by a singular integral operator and a BMO function on the variable Morrey spaces. Finally, we discuss the compactness of the commutator generated by a singular integral operator and a BMO function on the variable Morrey spaces.

Compactness of Commutators for Singular Integrals on Morrey Spaces

2012 ◽  
Vol 64 (2) ◽  
pp. 257-281 ◽  
Author(s):  
Yanping Chen ◽  
Yong Ding ◽  
Xinxia Wang
Keyword(s):  
Integral Operator ◽  
Compact Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Morrey Space ◽  
Singular Integrals ◽  
Morrey Spaces ◽  
Compact Set ◽  
Sufficient Condition

AbstractIn this paper we characterize the compactness of the commutator [b, T] for the singular integral operator on the Morrey spaces . More precisely, we prove that if , the -closure of , then [b, T] is a compact operator on the Morrey spaces for ∞ < p < ∞ and 0 < ⋋ < n. Conversely, if and [b, T] is a compact operator on the for some p (1 < p < ∞), then . Moreover, the boundedness of a rough singular integral operator T and its commutator [b, T] on are also given. We obtain a sufficient condition for a subset in Morrey space to be a strongly pre-compact set, which has interest in its own right.

Regularity in Morrey Spaces of Strong Solutions to Nondivergence Elliptic Equations with VMO Coefficients

1998 ◽  
Vol 5 (5) ◽  
pp. 425-440
Author(s):  
Dashan Fan ◽  
Shanzhen Lu ◽  
Dachun Yang
Keyword(s):  
Elliptic Equations ◽  
Singular Integrals ◽  
Strong Solutions ◽  
Morrey Spaces ◽  
Vmo Coefficients

Abstract In this paper, by means of the theories of singular integrals and linear commutators, the authors establish the regularity in Morrey spaces of strong solutions to nondivergence elliptic equations with VMO coefficients.

scholarly journals p-adic singular integrals and their commutators in generalized Morrey spaces

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hui X. Mo ◽  
Zhe Han ◽  
Liu Yang ◽  
Xiao J. Wang
Keyword(s):  
Singular Integrals ◽  
Morrey Spaces ◽  
Generalized Morrey Spaces

scholarly journals On the Boundedness of Singular Integrals in Morrey Spaces and its Preduals

2015 ◽  
Vol 22 (2) ◽  
pp. 462-490 ◽  
Author(s):  
Marcel Rosenthal ◽  
Hans-Jürgen Schmeisser
Keyword(s):  
Singular Integrals ◽  
Morrey Spaces
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