scholarly journals LpBounds for the Commutators of Oscillatory Singular Integrals with Rough Kernels

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yanping Chen ◽  
Kai Zhu
Keyword(s):  
Phase Function ◽  
Singular Integrals ◽  
Rough Kernels ◽  
Oscillatory Singular Integrals

We establish theLpboundedness for some commutators of oscillatory singular integrals with the kernel condition which was introduced by Grafakos and Stefanov. Our theorems contain various conditions on the phase function.

H1 boundedness of oscillatory singular integrals with degenerate phase functions

1994 ◽  
Vol 116 (2) ◽  
pp. 353-358
Author(s):  
Yibiao Pan
Keyword(s):  
Hardy Space ◽  
Singular Integral ◽  
Phase Function ◽  
Infinite Order ◽  
Singular Integrals ◽  
Integral Operators ◽  
Uniform Boundedness ◽  
Sufficient Condition ◽  
Oscillatory Singular Integrals ◽  
Phase Functions

AbstractIn this paper we study the uniform boundedness of oscillatory singular integral operators with degenerate phase functions on the Hardy space H1. The H1 boundedness was previously known when the phase function is nondegenerate. Here we obtain a sufficient condition for H1 boundedness which allows the phase function vanishing to infinite order.

scholarly journals Criterion of (Lp, Lr) boundedness for a class of multilinear oscillatory singular integrals

1998 ◽  
Vol 149 ◽  
pp. 33-51 ◽  
Author(s):  
Wengu Chen ◽  
Guoen Hu ◽  
Shanzhen Lu
Keyword(s):  
Singular Integrals ◽  
Multilinear Operators ◽  
Rough Kernels ◽  
Oscillatory Singular Integrals

Abstract.In this paper, we consider a kind of multilinear operators related to oscillatory singular integrals with rough kernels and give a criterion of certain boundedness for this kind of operators.

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 A note on maximal singular integrals with rough kernels

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiao Zhang ◽  
Feng Liu
Keyword(s):  
Singular Integral ◽  
Singular Integrals ◽  
Integral Operators ◽  
Maximal Operators ◽  
Rough Kernels ◽  
Lebesgue Spaces ◽  
Homogeneous Mapping ◽  
Recent Developments ◽  
Maximal Singular Integrals ◽  
Maximal Singular Integral

Abstract In this note we study the maximal singular integral operators associated with a homogeneous mapping with rough kernels as well as the corresponding maximal operators. The boundedness and continuity on the Lebesgue spaces, Triebel–Lizorkin spaces, and Besov spaces are established for the above operators with rough kernels in $H^{1}({\mathrm{S}}^{n-1})$ H 1 ( S n − 1 ) , which complement some recent developments related to rough maximal singular integrals.

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