Optimal extension of the Hausdorff-Young inequality

DOI10.1515/CRELLE.2008.054zbMath1166.46015OpenAlexW2153858298MaRDI QIDQ3524827

Werner J. Ricker, Gerd Mockenhaupt

Publication date: 15 September 2008

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/crelle.2008.054

zbMATH Keywords

Fourier transformoperatorHausdorff-Young inequalityoptimal domain

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Maximal functions, Littlewood-Paley theory (42B25) Linear operators on function spaces (general) (47B38) Vector-valued measures and integration (46G10) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (13)

Algebra structure for \(L^p\) of a vector measure ⋮ Integral extension of multiplier operators in \(A(G)\) ⋮ Optimal extension of Fourier multiplier operators in \(L^p(G)\) ⋮ Function spaces arising from kernel operators ⋮ Complex interpolation of operators and optimal domains ⋮ Fourier transform and convolutions on \(L^{p}\) of a vector measure on a compact Hausdorff abelian group ⋮ On the optimal domain of the Laplace transform ⋮ Solid extensions of the Cesàro operator on the Hardy space \(H^2(\mathbb D)\) ⋮ Salem sets in local fields, the Fourier restriction phenomenon and the Hausdorff-Young inequality ⋮ Explicit Salem sets, Fourier restriction, and metric Diophantine approximation in thep-adic numbers ⋮ Vector measures: Where are their integrals? ⋮ Optimal extension of the Fourier transform and convolution operator on compact groups ⋮ Inversion and extension of the finite Hilbert transform on \((-1,1)\)

Cites Work

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• Completeness of \(L^1\)-spaces for measures with values in complex vector spaces
• Rearrangement-invariant spaces of functions on LCA groups
• Inequalities for strongly singular convolution operators
• On singular monotonic functions whose spectrum has a given Hausdorff dimension
• Compactness properties of Sobolev imbeddings for rearrangement invariant norms
• Optimal domains and integral representations ofLp(G)-valued convolution operators via measures
• Optimal domains for the kernel operator associated with Sobolev's inequality
• NOTES ON THE THEORY OF SERIES (XIX): A PROBLEM CONCERNING MAJORANTS OF FOURIER SERIES

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