Displaying similar documents to “Recent developments in the theory of function spaces with dominating mixed smoothness”

On embedding theorems

Kolyada, Viktor I.

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This paper is devoted to embedding theorems for classes of functions of several variables. One of our main objectives is to give an analysis of some basic embeddings as well as to study relations between them. We also discuss some methods in this theory that were developed in the last decades. These methods are based on non-increasing rearrangements of functions, iterated rearrangements, estimates of sections of functions, related mixed norms, and molecular decompositions.

Non-Newtonian fluids and function spaces

Růžička, Michael, Diening, Lars

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In this note we give an overview of recent results in the theory of electrorheological fluids and the theory of function spaces with variable exponents. Moreover, we present a detailed and self-contained exposition of shifted N -functions that are used in the studies of generalized Newtonian fluids and problems with p -structure.

Traces of functions with a dominating mixed derivative in ℝ 3

Jan Vybíral, Winfried Sickel (2007)

Czechoslovak Mathematical Journal

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We investigate traces of functions, belonging to a class of functions with dominating mixed smoothness in ℝ 3 , with respect to planes in oblique position. In comparison with the classical theory for isotropic spaces a few new phenomenona occur. We shall present two different approaches. One is based on the use of the Fourier transform and restricted to p = 2 . The other one is applicable in the general case of Besov-Lizorkin-Triebel spaces and based on atomic decompositions.