Orlicz norm inequalities for operator-valued martingale transforms

2008 ◽  
Vol 78 (16) ◽  
pp. 2664-2670 ◽  
Author(s):  
Lin Yu
Keyword(s):  
Orlicz Norm ◽  
Norm Inequalities ◽  
Martingale Transforms

Tangent sequences in Orlicz and rearrangement invariant spaces

1996 ◽  
Vol 119 (1) ◽  
pp. 91-101 ◽  
Author(s):  
Paweł Hitczenko ◽  
Stephen J. Montgomery-Smith
Keyword(s):  
Random Variables ◽  
Universal Constant ◽  
Conditional Distributions ◽  
Orlicz Norm ◽  
Norm Inequalities ◽  
Rearrangement Invariant Spaces ◽  
Tangent Sequences ◽  
Invariant Spaces

AbstractLet (fn) and (gn) be two sequences of random variables adapted to an increasing sequence of σ-algebras (ℱn) such that the conditional distributions of fn and gn given ℱn coincide. Suppose further that the sequence (gn) is conditionally independent. Then it is known that where the number C is a universal constant. The aim of this paper is to extend this result to certain classes of Orlicz and rearrangement invariant spaces. This paper includes fairly general techniques for obtaining rearrangement invariant inequalities from Orlicz norm inequalities.

Weighted Norm Inequalities for a Maximal Operator in Some Subspace of Amalgams

2010 ◽  
Vol 53 (2) ◽  
pp. 263-277 ◽  
Author(s):  
Justin Feuto ◽  
Ibrahim Fofana ◽  
Konin Koua
Keyword(s):  
Maximal Operator ◽  
Fractional Integral ◽  
Space Of Homogeneous Type ◽  
Weighted Norm ◽  
Fractional Operator ◽  
Homogeneous Type ◽  
Weighted Norm Inequalities ◽  
Orlicz Norm ◽  
Lebesgue Spaces ◽  
Norm Inequalities

AbstractWe give weighted norm inequalities for the maximal fractional operator ℳq,β of Hardy– Littlewood and the fractional integral Iγ. These inequalities are established between (Lq, Lp)α(X, d, μ) spaces (which are superspaces of Lebesgue spaces Lα(X, d, μ) and subspaces of amalgams (Lq, Lp)(X, d, μ)) and in the setting of space of homogeneous type (X, d, μ). The conditions on the weights are stated in terms of Orlicz norm.

scholarly journals Weighted norm inequalities for a general maximal operator

1988 ◽  
Vol 26 (1-2) ◽  
pp. 327-340 ◽  
Author(s):  
Francisco J. Ruiz ◽  
Jose L. Torrea
Keyword(s):  
Maximal Operator ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities

scholarly journals Norm inequalities involving a special class of functions for sector matrices

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Davood Afraz ◽  
Rahmatollah Lashkaripour ◽  
Mojtaba Bakherad
Keyword(s):  
Special Class ◽  
Norm Inequalities ◽  
Class Of Functions

scholarly journals Two-weight norm inequalities for fractional integral operators with $A_{\lambda,\infty}$ weights

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Junren Pan ◽  
Wenchang Sun
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Type Estimate ◽  
Norm Inequalities ◽  
Fractional Integral Operators ◽  
New Class ◽  
Formula Type

Abstract In this paper, we introduce a new class of weights, the $A_{\lambda, \infty}$Aλ,∞ weights, which contains the classical $A_{\infty}$A∞ weights. We prove a mixed $A_{p,q}$Ap,q–$A_{\lambda,\infty}$Aλ,∞ type estimate for fractional integral operators.

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