Journal ArticleDOI
Fourier embeddings and Mihlin‐type multiplier theorems
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In this paper, theorems on singular convolution operators are combined with new Fourier embedding results to prove strong multiplier theorem on various function spaces (including Besov, Lebesgue-Bochner, and Hardy).Abstract:
Recent theorems on singular convolution operators are combined with new Fourier embedding results to prove strong multiplier theorems on various function spaces (including Besov, Lebesgue–Bochner, and Hardy). All the results apply to operator-valued multipliers acting on vector-valued functions, but some of them are new even in the scalar case. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)read more
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Wavelet transform for functions with values in UMD spaces
Cornelia Kaiser,Lutz Weis +1 more
TL;DR: In this paper, the authors extend the classical theory of the continuous and discrete wavelet transform to functions with values in UMD spaces, and obtain equivalent norms on Bochner spaces in terms of g-functions.
Journal ArticleDOI
Traces and embeddings of anisotropic function spaces
TL;DR: In this article, the trace spaces of a class of weighted function spaces of intersection type with mixed regularities were characterized and generalized to the fully inhomogeneous two-phase Stefan problem with Gibbs-Thomson correction.
Journal ArticleDOI
R -Boundedness of Smooth Operator-Valued Functions
Tuomas Hytönen,Mark Veraar +1 more
TL;DR: In this article, the authors studied the boundedness of operator families under cotype and type assumptions on X and Y and gave sufficient conditions for R$-boundedness of these families.
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R-boundedness of smooth operator-valued functions
Mark Veraar,Tuomas Hytönen +1 more
TL;DR: In this article, the authors studied the boundedness of operator families under cotype and type assumptions on X and Y and gave sufficient conditions for R$-boundedness of these families.
References
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Book
Theory of function spaces
TL;DR: In this article, the authors measure smoothness using Atoms and Pointwise Multipliers, Wavelets, Spaces on Lipschitz Domains, Wavelet and Sampling Numbers.
Book
Interpolation Spaces: An Introduction
Jöran Bergh,Jörgen Löfström +1 more
TL;DR: In this paper, the authors define the Riesz-Thorin Theorem as a necessary and sufficient condition for interpolation spaces, and apply it to approximate spaces in the context of vector spaces.
Book
Weighted Hardy Spaces
TL;DR: In this paper, the authors describe the decomposition of weights, including sharp maximal functions and functions in the upper half-space, as well as the Hardy spaces and the atomic decomposition.