Fourier transform and convolutions on \(L^{p}\) of a vector measure on a compact Hausdorff abelian group

DOI10.1007/s00041-012-9252-3zbMath1319.46031OpenAlexW2169189135MaRDI QIDQ485143

E. M. Navarrete, Enrique Alfonso Sánchez-Pérez, Jose M. Calabuig, Fernando Galaz-Fontes

Publication date: 9 January 2015

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00041-012-9252-3

zbMATH Keywords

Fourier transformconvolutionPettis integrabilitycountably additive vector measurespace of \(p\)-integrable functions

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Vector-valued measures and integration (46G10) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25)

Related Items (4)

Fourier analysis for vector-measures on compact abelian groups ⋮ On the optimal domain of the Laplace transform ⋮ Fourier analysis associated to a vector measure on a compact group ⋮ Convolution structures for an Orlicz space with respect to vector measures on a compact group

Cites Work

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• Complex interpolation of spaces of integrable functions with respect to a vector measure
• Optimal domain and integral extension of operators, acting in function spaces
• Fourier analysis with respect to bilinear maps
• Multiplication operators on vector measure Orlicz spaces
• Algebra structure for \(L^p\) of a vector measure
• Multiplication operators on spaces of integrable functions with respect to a vector measure
• Optimal extension of the Hausdorff-Young inequality
• Pettis integral and measure theory

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