Non-Newtonian fluids and function spaces

Růžička, Michael; Diening, Lars

Displaying similar documents to “Non-Newtonian fluids and function spaces”

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.

Recent developments in the theory of function spaces with dominating mixed smoothness

Schmeisser, Hans-Jürgen

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The aim of these lectures is to present a survey of some results on spaces of functions with dominating mixed smoothness. These results concern joint work with Winfried Sickel and Miroslav Krbec as well as the work which has been done by Jan Vybíral within his thesis. The first goal is to discuss the Fourier-analytical approach, equivalent characterizations with the help of derivatives and differences, local means, atomic and wavelet decompositions. Secondly, on this basis we study approximation...

Variable exponent Sobolev spaces with zero boundary values

Petteri Harjulehto (2007)

Mathematica Bohemica

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We study different definitions of the first order variable exponent Sobolev space with zero boundary values in an open subset of $ℝ^{n}$ .

Alternative characterisations of Lorentz-Karamata spaces

David Eric Edmunds, Bohumír Opic (2008)

Czechoslovak Mathematical Journal

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We present new formulae providing equivalent quasi-norms on Lorentz-Karamata spaces. Our results are based on properties of certain averaging operators on the cone of non-negative and non-increasing functions in convenient weighted Lebesgue spaces. We also illustrate connections between our results and mapping properties of such classical operators as the fractional maximal operator and the Riesz potential (and their variants) on the Lorentz-Karamata spaces.