scholarly journals Some Weighted Estimates for Multilinear Fourier Multiplier Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Zengyan Si
Keyword(s):  
Sobolev Spaces ◽  
Fourier Multiplier ◽  
Multilinear Operators ◽  
Multiplier Theorem ◽  
Weighted Estimates ◽  
Fourier Multiplier Operators ◽  
Multiplier Operators

We first provide a weighted Fourier multiplier theorem for multilinear operators which extends Theorem 1.2 in Fujita and Tomita (2012) by usingLr-based Sobolev spaces (1<r≤2). Then, by using a different method, we obtain a result parallel to Theorem 6.2 which is an improvement of Theorem 1.2 under assumption (i) in Fujita and Tomita (2012).

scholarly journals H-Distributions: An Extension ofH-Measures to anLp-LqSetting

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Nenad Antonić ◽  
Darko Mitrović
Keyword(s):  
Fourier Multiplier ◽  
Fourier Multiplier Operators ◽  
Multiplier Operators

We use the continuity of Fourier multiplier operators onLpto introduce theH-distributions—an extension ofH-measures in theLpframework. We apply theH-distributions to obtain anLpversion of the localisation principle and reprove the MuratLp-Lp′variant of div-curl lemma.

scholarly journals Smoothness of functions versus smoothness of approximation processes

2020 ◽  
Vol 10 (03) ◽  
pp. 2030002
Author(s):  
Yu. S. Kolomoitsev ◽  
S. Yu. Tikhonov
Keyword(s):  
Banach Spaces ◽  
Fourier Multiplier ◽  
Moduli Of Smoothness ◽  
Geometric Properties ◽  
Wavelet Approximation ◽  
Multiplier Theorems ◽  
Fourier Multiplier Operators ◽  
Multiplier Operators ◽  
Comprehensive Study

We provide a comprehensive study of interrelations between different measures of smoothness of functions on various domains and smoothness properties of approximation processes. Two general approaches to this problem have been developed: The first based on geometric properties of Banach spaces and the second on Littlewood–Paley and Hörmander-type multiplier theorems. In particular, we obtain new sharp inequalities for measures of smoothness given by the [Formula: see text]-functionals or moduli of smoothness. As examples of approximation processes we consider best polynomial and spline approximations, Fourier multiplier operators on [Formula: see text], [Formula: see text], [Formula: see text], nonlinear wavelet approximation, etc.

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