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Prostory funkcí, diferenciální operátory a nelineární analýza
Drábek, P. ; Rákosník, Jiří
The proceedings contain four of the invited main lectures and 23 selected contributions by the participants. All published papers were subject to the standard referee procedure. The conference was the sixth in the series of international meetings organized under the same name alternatively in Finland, Germany and Czech Republic since 1988. This conference was devoted to the seventieth birthday of Prof. Alois Kufner, the founder of the Czech school on the theory of function spaces.
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Limitní reiterační vzorce pro reálnou interpolaci a aplikaci
Opic, Bohumír
The aim of the paper is to describe reiteration formulal with the limiting value 0=1 for a real interpolation method. Limiting reiteration can be used to investigate a behaviour of linear and some quasi-linear operators in limiting situations. Results are applied to describe the limiting behaviour of the fractional maximal operator and to derive sharp limiting embeddings of Sobolev-Orlicz spaces W1 Ln(log L).alpha.(.omega.). In particular, if .alpha.= 0, we obtain the embedding which is due to Brézis and Wainger.
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Extrapolace. Aktuální výsledky a problémy
Krbec, Miroslav
This paper is deals with several recent extrapolation results from the recent author´s papers and tackles further the relations of the spaces involved. First, very simple and transparent proofs of extrapolation theorems of Yano type in Lorentz spaces is given, unifiying classical and new results. Second, the variation of the classical situation near arbitrary L_p is studied and the answer is icen in terms of Zygmund, Lorentz-Zygmund and small Lebesgue spaces.
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Sobolev inequality with variable exponent
Rákosník, Jiří
Recently, an increasing attention has been payed to partial differential equations and variational integrals involving coefficients of nonstandard growth. A natural tool to handle some of the related problems may be theory of spaces of functions integrable with variable exponent. The paper discusses the Sobolev inequality in this context and shows that it holds if the exponentfunction is Lipschitz-continuous.
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