scholarly journals Weighted Norm Inequalities for Multilinear Fourier Multipliers with Mixed Norm

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Mai Fujita
Keyword(s):  
Sobolev Space ◽  
Fourier Multipliers ◽  
Mixed Norm ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Sobolev Regularity

In this paper, weighted norm inequalities for multilinear Fourier multipliers satisfying Sobolev regularity with mixed norm are discussed. Our result can be understood as a generalization of the result by Fujita and Tomita by using the L r -based Sobolev space, 1 < r ≤ 2 with mixed norm.

Weighted Fourier Transform Inequalities via Mixed Norm Hausdorff-Young Inequalities

1994 ◽  
Vol 46 (3) ◽  
pp. 586-601 ◽  
Author(s):  
Joseph D. Lakey
Keyword(s):  
Fourier Transform ◽  
Lorentz Spaces ◽  
Mixed Norm ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Natural Class ◽  
Norm Inequalities ◽  
The Fourier Transform ◽  
Amalgam Spaces

AbstractWiener-Lorentz amalgam spaces are introduced and some of their interpolation theoretic properties are discussed. We prove Hausdorff-Young theorems for these spaces unifying and extending Hunt's Hausdorff-Young theorem for Lorentz spaces and Holland's theorem for amalgam spaces. As consequences we prove weighted norm inequalities for the Fourier transform and show how these inequalities fit into a natural class of weighted Fourier transform estimates

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
Sign in / Sign up

Export Citation Format

Share Document