scholarly journals Maximal operators with rough kernels on product domains

2005 ◽  
Vol 311 (1) ◽  
pp. 338-351 ◽  
Author(s):  
Ahmad Al-Salman
Keyword(s):  
Maximal Operators ◽  
Rough Kernels ◽  
Product Domains

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.

scholarly journals Marcinkiewicz integrals along subvarieties on product domains

2004 ◽  
Vol 2004 (72) ◽  
pp. 4001-4011
Author(s):  
Ahmad Al-Salman
Keyword(s):  
Integral Operators ◽  
Marcinkiewicz Integral ◽  
Rough Kernels ◽  
Marcinkiewicz Integrals ◽  
Product Domains

We study theLpmapping properties of a class of Marcinkiewicz integral operators on product domains with rough kernels supported by subvarieties.

L p bounds for singular integrals with rough kernels on product domains

2011 ◽  
Vol 28 (1) ◽  
pp. 133-144 ◽  
Author(s):  
Li Ma ◽  
Da Shan Fan ◽  
Huo Xiong Wu
Keyword(s):  
Singular Integrals ◽  
Rough Kernels ◽  
Product Domains

scholarly journals Generalized parabolic Marcinkiewicz integrals associated with polynomial compound curves with rough kernels

2020 ◽  
Vol 53 (1) ◽  
pp. 44-57
Author(s):  
Mohammed Ali ◽  
Qutaibeh Katatbeh
Keyword(s):  
Integral Operators ◽  
Marcinkiewicz Integral ◽  
Rough Kernels ◽  
Marcinkiewicz Integrals ◽  
Natural Extensions ◽  
Parametric Marcinkiewicz Integral ◽  
Weaker Conditions

AbstractIn this article, we study the generalized parabolic parametric Marcinkiewicz integral operators { {\mathcal M} }_{{\Omega },h,{\Phi },\lambda }^{(r)} related to polynomial compound curves. Under some weak conditions on the kernels, we establish appropriate estimates of these operators. By the virtue of the obtained estimates along with an extrapolation argument, we give the boundedness of the aforementioned operators from Triebel-Lizorkin spaces to Lp spaces under weaker conditions on Ω and h. Our results represent significant improvements and natural extensions of what was known previously.

Sign in / Sign up

Export Citation Format

Share Document