Convolution Calderón-Zygmund singular integral operators with rough kernels

1999 ◽  
pp. 119-143 ◽  
Author(s):  
L. Grafakos ◽  
A. Stefanov
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Rough Kernels

On a Class of Singular Integral Operators With Rough Kernels

2006 ◽  
Vol 49 (1) ◽  
pp. 3-10 ◽  
Author(s):  
Ahmad Al-Salman
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Maximal Functions ◽  
Rough Kernels ◽  
Block Spaces ◽  
Size Condition

AbstractIn this paper, we study the Lp mapping properties of a class of singular integral operators with rough kernels belonging to certain block spaces. We prove that our operators are bounded on Lp provided that their kernels satisfy a size condition much weaker than that for the classical Calderón–Zygmund singular integral operators. Moreover, we present an example showing that our size condition is optimal. As a consequence of our results, we substantially improve a previously known result on certain maximal functions.

scholarly journals On the Theory of Multilinear Singular Operators with Rough Kernels on the Weighted Morrey Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Sha He ◽  
Xiangxing Tao
Keyword(s):  
Singular Integral ◽  
Fractional Integral ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Singular Integral Operators ◽  
Multilinear Operators ◽  
Rough Kernels ◽  
Fractional Integral Operators ◽  
Weighted Morrey Spaces ◽  
Maximal Singular Integral

We study some multilinear operators with rough kernels. For the multilinear fractional integral operatorsTΩ,αAand the multilinear fractional maximal integral operatorsMΩ,αA, we obtain their boundedness on weighted Morrey spaces with two weightsLp,κ(u,v)whenDγA∈Λ˙β  (|γ|=m-1)orDγA∈BMO  (|γ|=m-1). For the multilinear singular integral operatorsTΩAand the multilinear maximal singular integral operatorsMΩA, we show they are bounded on weighted Morrey spaces with two weightsLp,κ(u,v)ifDγA∈Λ˙β  (|γ|=m-1)and bounded on weighted Morrey spaces with one weightLp,κ(w)ifDγA∈BMO  (|γ|=m-1)form=1,2.

scholarly journals Singular integrals related to homogeneous mapping with rough kernels on product spaces

2008 ◽  
Vol 39 (2) ◽  
pp. 165-176 ◽  
Author(s):  
H. Al-Qassem ◽  
M. Ali
Keyword(s):  
Singular Integral ◽  
Singular Integrals ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Product Spaces ◽  
Rough Kernels ◽  
Homogeneous Mapping ◽  
Block Spaces ◽  
Homogeneous Mappings

In this paper, we study the $ L^{p} $ mapping properties of singular integral operators related to homogeneous mappings on product spaces with kernels which belong to block spaces. Our results extend as well as improve some known results on singular integrals.

COMPACTNESS FOR HIGHER ORDER COMMUTATORS OF OSCILLATORY SINGULAR INTEGRAL OPERATORS

2009 ◽  
Vol 20 (09) ◽  
pp. 1137-1146 ◽  
Author(s):  
HEPING LIU ◽  
LIN TANG
Keyword(s):  
Singular Integral ◽  
Integral Operators ◽  
Higher Order ◽  
Singular Integral Operators ◽  
Rough Kernels ◽  
Oscillatory Singular Integral

In this paper, the authors study the compactness for higher order commutators of oscillatory singular integral operators with rough kernels satisfying Lq-Dini conditions.

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