How smooth is almost every function in a Sobolev space?

DOI10.4171/RMI/469zbMath1155.28302OpenAlexW1998045092MaRDI QIDQ879633

Stéphane Jaffard, Aurélia Fraysse

Publication date: 14 May 2007

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmi/1161871351

zbMATH Keywords

prevalenceSobolev spacesHausdorff dimensionBesov spacesHölder regularitywavelet basesHaar-null setsmultifractal functions

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Fractals (28A80) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20) Classification of real functions; Baire classification of sets and functions (26A21)

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