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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, ((1957), Dover: Dover New York), 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, ((1955)), 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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