scholarly journals A characterization of two weight norm inequalities for maximal singular integrals with one doubling measure

2012 ◽  
Vol 5 (1) ◽  
pp. 1-60 ◽  
Author(s):  
Michael Lacey ◽  
Eric Sawyer ◽  
Ignacio Uriarte-Tuero
Keyword(s):  
Singular Integrals ◽  
Doubling Measure ◽  
Norm Inequalities ◽  
Maximal Singular Integrals

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.

A Characterization of two Weight Norm Inequalities for One-Sided Operators of Fractional Type

1997 ◽  
Vol 49 (5) ◽  
pp. 1010-1033 ◽  
Author(s):  
Maria Lorente
Keyword(s):  
Fractional Integral ◽  
Norm Inequalities ◽  
Fractional Type

AbstractIn this paper we give a characterization of the pairs of weights (ω, v) such that T maps Lp(v) into Lq(ω),where T is a general one-sided operator that includes as a particular case theWeyl fractional integral. As an applicationwe solve the following problem: given a weight v, when is there a nontrivial weight ω such that T maps Lp(v) into Lq(ω)?

scholarly journals Boundedness of Singular Integrals on Hardy Type Spaces Associated with Schrödinger Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Jianfeng Dong ◽  
Jizheng Huang ◽  
Heping Liu
Keyword(s):  
Molecular Characterization ◽  
Singular Integral ◽  
Maximal Function ◽  
Singular Integrals ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Hardy Type ◽  
Type Spaces ◽  
Reverse Hölder

LetL=-Δ+Vbe a Schrödinger operator onRn,n≥3, whereV≢0is a nonnegative potential belonging to the reverse Hölder classBn/2. The Hardy type spacesHLp, n/(n+δ) <p≤1,for someδ>0, are defined in terms of the maximal function with respect to the semigroup{e-tL}t>0. In this paper, we investigate the bounded properties of some singular integral operators related toL, such asLiγand∇L-1/2, on spacesHLp. We give the molecular characterization ofHLp, which is used to establish theHLp-boundedness of singular integrals.

scholarly journals Two weight norm inequalities for communtators of one-sided singular integrals and the one-sided discrete square function

2005 ◽  
Vol 79 (1) ◽  
pp. 77-94 ◽  
Author(s):  
M. Lorente ◽  
M. S. Riveros
Keyword(s):  
Singular Integrals ◽  
Square Function ◽  
Strong Type ◽  
Norm Inequalities ◽  
The One

AbstractThe purpose of this paper is to prove strong type inequalities with pairs of related weights for commutators of one-sided singular integrals (given by a Calderón-Zygmund kernel with support in (-∞, 0)) and the one-sided discrete square function. The estimate given by C. Segovia and J. L. Torrea is improved for these one-sided operators giving a wider class of weights for which the inequality holds.

scholarly journals On weighted weak type norm inequalities for one-sided oscillatory singular integrals

2011 ◽  
Vol 207 (2) ◽  
pp. 137-151 ◽  
Author(s):  
Zunwei Fu ◽  
Shanzhen Lu ◽  
Shuichi Sato ◽  
Shaoguang Shi
Keyword(s):  
Singular Integrals ◽  
Weak Type ◽  
Norm Inequalities ◽  
Oscillatory Singular Integrals
Sign in / Sign up

Export Citation Format

Share Document