Weighted Norm Estimates for the Fourier Transform with a Pair of Weights

1990 ◽  
Vol 318 (1) ◽  
pp. 355 ◽  
Author(s):  
Jan-Olov Stromberg ◽  
Richard L. Wheeden
Keyword(s):  
Fourier Transform ◽  
Weighted Norm ◽  
Norm Estimates ◽  
The Fourier Transform

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

Weighted Restriction for Curves

1993 ◽  
Vol 36 (1) ◽  
pp. 87-95 ◽  
Author(s):  
Joseph D. Lakey
Keyword(s):  
Fourier Transform ◽  
Weight Function ◽  
Weighted Norm ◽  
Two Dimensional ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Restriction Theorems ◽  
Nonnegative Weight ◽  
The Fourier Transform ◽  
Image Position

AbstractWe prove weighted norm inequalities for the Fourier transform of the formwhere v is a nonnegative weight function on ℝd and ψ: [— 1,1 ] —> ℝd is a nondegenerate curve. Our results generalize unweighted (i.e. v = 1) restriction theorems of M. Christ, and two-dimensional weighted restriction theorems of C. Carton-Lebrun and H. Heinig.

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