Milne, Stephen C. Peano curves and smoothness of functions. (English) Zbl 0449.26015 Adv. Math. 35, 129-157 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 15 Documents MSC: 26D15 Inequalities for sums, series and integrals 28D05 Measure-preserving transformations 28A99 Classical measure theory Keywords:higher-dimensional analogue of an integral; inequality of Garsia and Rodemich; nonincreasing rearrangement; Lipschitzian and measure preserving properties of Peano curves Citations:Zbl 0274.26006 PDFBibTeX XMLCite \textit{S. C. Milne}, Adv. Math. 35, 129--157 (1980; Zbl 0449.26015) 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.