General monotonicity, interpolation of operators, and applications
S.M. Grigoriev, Y. Sagher, T.R. Savage
TL;DR
This paper explores the equivalence of L(p,q)-norms of general monotone functions and their Fourier transforms, utilizing interpolation properties of monotone function cones to extend previous work in harmonic analysis.
Contribution
It establishes the equivalence of L(p,q)-norms for general monotone functions and their Fourier transforms, advancing the understanding of their interpolation properties.
Findings
Proves the equivalence of L(p,q)-norms for monotone functions and Fourier transforms.
Utilizes interpolation properties of cones of general monotone functions.
Builds upon and extends previous work by Tikhonov, Liflyand, Booton, and others.
Abstract
We continue the work of S. Tikhonov, E. Liflyand, B. Booton, and others, proving the equivalence of L(p,q)-norms of general monotone functions and of their Fourier transforms. The main tool in this work is the interpolation properties of cones of general monotone functions in L(p,q)-norms.
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Taxonomy
TopicsApproximation Theory and Sequence Spaces · Mathematical Analysis and Transform Methods · Mathematical Inequalities and Applications