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Peano curves and smoothness of functions. (English) Zbl 0449.26015


MSC:

26D15 Inequalities for sums, series and integrals
28D05 Measure-preserving transformations
28A99 Classical measure theory

Citations:

Zbl 0274.26006
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Full Text: DOI

References:

[1] Garsia, A.M, Combinatorial inequalities and smoothness of functions, Bull. amer. math. soc., 82, 157-170, (1976) · Zbl 0351.26005
[2] Garsia, A.M; Rodemich, E, Monotonicity of certain functionals under rearrangement, Ann. inst. Fourier, 24, 69-116, (1974) · Zbl 0274.26006
[3] Hobson, X, The theory of functions of a real variable, (), 451-458
[4] Jessen, B, The theory of integration in a space of an infinite number of dimensions, Acta math., 62, 250-271, (1934) · Zbl 0010.20004
[5] Moore, E.H, On certain crinkly curves, Trans. amer. math. soc., 1, 72-90, (1900) · JFM 31.0564.03
[6] Peano, G, Sur une courbe qui remplit toute une aire plane, Math. ann., 36, 157-160, (1890) · JFM 22.0405.01
[7] Riesz, F; Nagy, B, Functional analysis, (), 81-104, New York
[8] Salem, R, Lacunary power series and Peano curves, Duke math. J., 12, 569-578, (1945) · Zbl 0060.20402
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