scholarly journals A sharp form of the Marcinkiewicz interpolation theorem for Orlicz spaces

2020 ◽  
Vol 255 (2) ◽  
pp. 109-158
Author(s):  
Ron Kerman ◽  
Rama Rawat ◽  
Rajesh K. Singh
Keyword(s):  
Orlicz Spaces ◽  
Interpolation Theorem ◽  
Sharp Form ◽  
Marcinkiewicz Interpolation Theorem

scholarly journals Atomic decompositions of Lorentz martingale spaces and applications

2009 ◽  
Vol 7 (2) ◽  
pp. 153-166 ◽  
Author(s):  
Jiao Yong ◽  
Peng Lihua ◽  
Liu Peide
Keyword(s):  
Atomic Decomposition ◽  
Weak Type ◽  
Interpolation Theorem ◽  
Sublinear Operator ◽  
Sufficient Condition ◽  
Atomic Decompositions ◽  
Type Interpolation ◽  
Marcinkiewicz Interpolation Theorem ◽  
Decomposition Theorems

In the paper we present three atomic decomposition theorems of Lorentz martingale spaces. With the help of atomic decomposition we obtain a sufficient condition for sublinear operator defined on Lorentz martingale spaces to be bounded. Using this sufficient condition, we investigate some inequalities on Lorentz martingale spaces. Finally we discuss the restricted weak-type interpolation, and prove the classical Marcinkiewicz interpolation theorem in the martingale setting.

scholarly journals Theory of discrete Muckenhoupt weights and discrete Rubio de Francia extrapolation theorems

2021 ◽  
pp. 17-17
Author(s):  
S.H. Saker ◽  
R.P. Agarwal
Keyword(s):  
Maximal Operator ◽  
Interpolation Theorem ◽  
The Self ◽  
Muckenhoupt Weights ◽  
Extrapolation Theorem ◽  
Marcinkiewicz Interpolation Theorem ◽  
Littlewood Maximal Operator

In this paper, we will prove a discrete Rubio De Francia extrapolation theorem in the theory of discrete Ap-Muckenhoupt weights for which the discrete Hardy-Littlewood maximal operator is bounded on lpw (Z+). The results will be proved by employing the self-improving property of the discrete Ap-Muckenhoupt weights and the Marcinkiewicz Interpolation Theorem.

scholarly journals The multilinear Marcinkiewicz interpolation theorem revisited: The behavior of the constant

2012 ◽  
Vol 262 (5) ◽  
pp. 2289-2313 ◽  
Author(s):  
Loukas Grafakos ◽  
Liguang Liu ◽  
Shanzhen Lu ◽  
Fayou Zhao
Keyword(s):  
Interpolation Theorem ◽  
Marcinkiewicz Interpolation Theorem

Weighted norm inequalities for the Hankel- and -transformations

1986 ◽  
Vol 103 (3-4) ◽  
pp. 325-333 ◽  
Author(s):  
S. A. Emara ◽  
H. P. Heinig
Keyword(s):  
Interpolation Theorem ◽  
Linear Operators ◽  
Weight Functions ◽  
Weighted Estimate ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Hankel Transformation ◽  
Negative Weight ◽  
Marcinkiewicz Interpolation Theorem ◽  
Image Position

SynopsisWe give conditions on pairs of non-negative weight functions u and v which are sufficient that, for 1<p, q <∞,where T is the Hankel-or the K-transformation.The proofs are based on a weighted Marcinkiewicz interpolation theorem for linear operators. In the case that T is the Hankel transformation and 1<p≦q <∞, the result is similar to a weighted estimate of Heywood and Rooney [9], but with different weight conditions.

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