Hans Triebel

Fractals and Spectra: Related to Fourier Analysis and Function Spaces

This book deals with the symbiotic relationship between the theory of function spaces, fractal geometry, and spectral theory of (fractal) pseudodifferential operators as it has emerged quite recently. Most of the presented material is published here for the first time.

Local function spaces, heat and Navier-Stokes equations

analyse fonctionnelle # analyse harmonique # equation aux derivees partielles # mecanique des fluides # equation de Navier-Stokes # equation de la chaleur # ondelette

Spectral theory for isotropic fractal drums

Abstract We study the behaviour of eigenvalues in problems which correspond to the vibrations of a drum, the whole mass of which is concentrated on a fractal subset of the drum.

Characterizations of Besov-Hardy-Sobolev spaces: a unified approach

Revue de la theorie des normes et des quasi normes equivalentes dans les espaces de Besov-Hardy-Sobolev. Unification des differentes caracterisations

Eigenfrequencies of isotropic fractal drums

We study the behaviour of eigenvalues in problems which correspond to the vibrations of a drum, the whole mass of which is concentrated on a fractal subset of the drum.

Characterizations of Besov-Hardy-Sobolev spaces via harmonic functions, temperatures, and related means

If s > 0, 1 <p < co and 1 < q < co, then there exists a large number of equivalent characterizations of the (nowadays classical) Besov (or Lipschitz) spaces B&, defined on the Euclidean n-space R,. One can take one of these characterizations as a definition; e.g., Bi,, (under the above restrictions for s, p and q) is the collection of all complex-valued functions f(x) E L, (the usual L,-spaces on R,) such that

Full length article: Entropy and approximation numbers of limiting embeddings; an approach via Hardy inequalities and quadratic forms

This paper deals with entropy numbers and approximation numbers for compact embeddings of weighted Sobolev spaces into Lebesgue spaces in limiting situations. This work is based on related Hardy inequalities and the spectral theory of some degenerate elliptic operators.

General function spaces. III(SpacesBp,qg(x) andFp,qg(x), 1<p<∞: basic properties)

AbstractqNАстОьЩАь РАБОтА (А тАк жЕ ЕЕ пРОДОлжЕНИЕ — РА БОтА «ОБЩИЕ ФУНкцИОНАльН ыЕ пРО-стРАНстВА, IV») пОсВьЩЕНА ИсслЕДОВ АНИУ БАНАхОВых пРОст РАНстВBp, qg(x) ИFp,qg(x) РАспРЕДЕлЕНИИ (ОБОБЩЕННых) ВRn. В спЕц ИАльНых слУЧАьх ЁтИ пРОстРАНстВА РОДстВ ЕННы ИжВЕстНыМ клАсс АМ сОБОлЕВА—лЕБЕгА—БЕ сОВА, ИжОтРОпНыМ И АНИ жОтРОпНыМ. жДЕсь РАссМАтРИВАУт сь слЕДУУ-ЩИЕ сВОИстВА: плОтНОсть г лАДкИх ФУНкцИИ, ЁкВИВ АлЕНтНыЕ НОРМы, ИНтЕРпОльцИь, В клУЧЕНИь И сРАВНЕНИь. ОБЩИЕ ФУНкцИОНАльНы Е пРОстРАНстВА. III (пРОстРАНстВАBp,qg(x) ИFp,qg(x), 1

The critical case

By the terminology of (10.6) the critical case covers the spaces