scholarly journals Weighted norm inequalities for a class of rough singular integrals

2005 ◽  
Vol 2005 (5) ◽  
pp. 657-669
Author(s):  
H. M. Al-Qassem
Keyword(s):  
Integral Operator ◽  
Singular Integral Operator ◽  
Singular Integral ◽  
Singular Integrals ◽  
Singular Operator ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities

Weighted norm inequalities are proved for a rough homogeneous singular integral operator and its corresponding maximal truncated singular operator. Our results are essential improvements as well as extensions of some known results on the weighted boundedness of singular integrals.

Weighted Norm Inequalities for Fractional Integral Operators With Rough Kernel

1998 ◽  
Vol 50 (1) ◽  
pp. 29-39 ◽  
Author(s):  
Yong Ding ◽  
Shanzhen Lu
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Rough Kernel ◽  
Degree Zero ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Fractional Integral Operators ◽  
Image Position

AbstractGiven function Ω on ℝn , we define the fractional maximal operator and the fractional integral operator by and respectively, where 0 < α < n. In this paper we study the weighted norm inequalities of MΩα and TΩα for appropriate α, s and A(p, q) weights in the case that Ω∈ Ls(Sn-1)(s> 1), homogeneous of degree zero.

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.

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