scholarly journals Maximal operators on variable Lebesgue spaces with weights related to oscillations of Carleson curves

2009 ◽  
Vol 283 (1) ◽  
pp. 85-93 ◽  
Author(s):  
Alexei Yu. Karlovich
Keyword(s):  
Maximal Operators ◽  
Lebesgue Spaces ◽  
Variable Lebesgue Spaces

scholarly journals Two-Weight Norm Inequality for the One-Sided Hardy-Littlewood Maximal Operators in Variable Lebesgue Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Caiyin Niu ◽  
Zongguang Liu ◽  
Panwang Wang
Keyword(s):  
Liouville Operator ◽  
Norm Inequality ◽  
Maximal Operators ◽  
Weight Norm Inequality ◽  
Weyl Operator ◽  
Lebesgue Spaces ◽  
Norm Inequalities ◽  
Variable Lebesgue Spaces ◽  
The One

The authors establish the two-weight norm inequalities for the one-sided Hardy-Littlewood maximal operators in variable Lebesgue spaces. As application, they obtain the two-weight norm inequalities of variable Riemann-Liouville operator and variable Weyl operator in variable Lebesgue spaces on bounded intervals.

Off-diagonal extrapolation on mixed variable Lebesgue spaces and its applications to strong fractional maximal operators

2020 ◽  
Vol 27 (4) ◽  
pp. 637-647
Author(s):  
Jian Tan
Keyword(s):  
Maximal Operators ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Lebesgue Spaces ◽  
Norm Inequalities ◽  
Variable Lebesgue Spaces ◽  
Vector Valued ◽  
Mixed Variable

AbstractWe establish off-diagonal extrapolation on mixed variable Lebesgue spaces. As its applications, we obtain the boundedness for strong fractional maximal operators. The vector-valued analogies are also considered. Additionally, the Littlewood–Paley characterization for mixed variable Lebesgue spaces is also established with the help of weighted norm inequalities and extrapolation.

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.

New variable martingale Hardy spaces

2021 ◽  
pp. 1-29
Author(s):  
Yong Jiao ◽  
Dan Zeng ◽  
Dejian Zhou
Keyword(s):  
Brownian Motion ◽  
Hardy Space ◽  
Hardy Spaces ◽  
Stochastic Integral ◽  
Lebesgue Spaces ◽  
Type Space ◽  
Variable Lebesgue Spaces ◽  
Martingale Inequalities

We investigate various variable martingale Hardy spaces corresponding to variable Lebesgue spaces $\mathcal {L}_{p(\cdot )}$ defined by rearrangement functions. In particular, we show that the dual of martingale variable Hardy space $\mathcal {H}_{p(\cdot )}^{s}$ with $0<p_{-}\leq p_{+}\leq 1$ can be described as a BMO-type space and establish martingale inequalities among these martingale Hardy spaces. Furthermore, we give an application of martingale inequalities in stochastic integral with Brownian motion.

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