On vector-valued Fourier multiplier theorems

Frank Zimmermann

Displaying similar documents to “On vector-valued Fourier multiplier theorems”

A class of Fourier multipliers on H¹(ℝ²)

Michał Wojciechowski (2000)

Studia Mathematica

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An integral criterion for being an $H^{1} (ℝ^{2})$ Fourier multiplier is proved. It is applied in particular to suitable regular functions which depend on the product of variables.

Schauder decompositions and multiplier theorems

P. Clément, B. de Pagter, F. Sukochev, H. Witvliet (2000)

Studia Mathematica

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We study the interplay between unconditional decompositions and the R-boundedness of collections of operators. In particular, we get several multiplier results of Marcinkiewicz type for $L^{p}$ -spaces of functions with values in a Banach space X. Furthermore, we show connections between the above-mentioned properties and geometric properties of the Banach space X.

On convergence of Fourier series of functions of generalized bounded variation

Daniel Waterman (1972)

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A characterization of localized Bessel potential spaces and applications to Jacobi and Henkel multipliers

George Gasper, Walter Trebels (1979)

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Absolute convergence of Fourier series of a function of Wiener’s class $V_{p}$

Siddiqi, Rafat N. (1979)

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A note on Fourier coefficients

B. N. Varma (1969)

Rendiconti del Seminario Matematico della Università di Padova

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On unconditional convergence of Haar series

G. Tkebuchava (1979)

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Almost everywhere convergence of Walsh Fourier series of $H^{1}$ -functions

N. Ladhawala, D. Pankratz (1976)

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Note on the absolute convergence of Fourier series of a function of Wiener’s class $V_{r}$

Okuyama, Yasuo (1983-1984)

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Spectral decompositions and harmonic analysis on UMD spaces

Earl Berkson, T. Gillespie (1994)

Studia Mathematica

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We develop a spectral-theoretic harmonic analysis for an arbitrary UMD space X. Our approach utilizes the spectral decomposability of X and the multiplier theory for $L_{X}^{p}$ to provide on the space X itself analogues of the classical themes embodied in the Littlewood-Paley Theorem, the Strong Marcinkiewicz Multiplier Theorem, and the M. Riesz Property. In particular, it is shown by spectral integration that classical Marcinkiewicz multipliers have associated transforms acting on X. ...