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Combinatorial inequalities and smoothness of functions. (English) Zbl 0351.26005


MSC:

26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
26D15 Inequalities for sums, series and integrals
42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series
05A20 Combinatorial inequalities
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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[1] Adriano M. Garsia, On the smoothness of functions satisfying certain integral inequalities, Functional Analysis (Proc. Sympos., Monterey, Calif., 1969) Academic Press, New York, 1969, pp. 127 – 162.
[2] Adriano M. Garsia, A remarkable inequality and the uniform convergence of Fourier series, Indiana Univ. Math. J. 25 (1976), no. 1, 85 – 102. · Zbl 0324.42005
[3] A. M. Garsia and P. DeLand, Moduli of continuity for exponential Lipschitz classes (to appear).
[4] A. M. Garsia and S. Milne, Peano curves and smoothness of functions (to appear).
[5] A. M. Garsia and E. Rodemich, Monotonicity of certain functionals under rearrangement, Ann. Inst. Fourier (Grenoble) 24 (1974), no. 2, vi, 67 – 116 (English, with French summary). Colloque International sur les Processus Gaussiens et les Distributions Aléatoires (Colloque Internat. du CNRS, No. 222, Strasbourg, 1973). · Zbl 0274.26006
[6] A. M. Garsia, E. Rodemich, and H. Rumsey Jr., A real variable lemma and the continuity of paths of some Gaussian processes, Indiana Univ. Math. J. 20 (1970/1971), 565 – 578. · Zbl 0252.60020
[7] R. K. Getoor and H. Kesten, Continuity of local times for Markov processes, Compositio Math. 24 (1972), 277 – 303. · Zbl 0293.60069
[8] Charles A. Greenhall, Growth and continuity of functions satisfying quadratic integral inequalities, Indiana Univ. Math. J. 21 (1971/1972), 157 – 175. · Zbl 0212.08604
[9] Naresh C. Jain and M. B. Marcus, Sufficient conditions for the continuity of stationary Gaussian processes and applications to random series of functions, Ann. Inst. Fourier (Grenoble) 24 (1974), no. 2, vi, 117 – 141 (English, with French summary). Colloque International sur les Processus Gaussiens et les Distributions Aléatoires (Colloque Internat. du CNRS, No. 222, Strasbourg, 1973). · Zbl 0283.60041
[10] L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa (3) 13 (1959), 115 – 162. · Zbl 0088.07601
[11] T. W. Park, Sobolov type inequalities and path continuity of L (to appear).
[12] Christopher Preston, Continuity properties of some Gaussian processes, Ann. Math. Statist. 43 (1972), 285 – 292. · Zbl 0268.60044
[13] Herbert Taylor, Rearrangements of incidence tables, J. Combinatorial Theory Ser. A 14 (1973), 30 – 36. · Zbl 0257.05019
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