A Morrey-Nikol′skiĭ inequality
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- by James Ross
- Proc. Amer. Math. Soc. 78 (1980), 97-102
- DOI: https://doi.org/10.1090/S0002-9939-1980-0548092-0
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Abstract:
An inequality of Sobolev type is proved which unifies some work of Nikol’skiĭ on fractional derivatives and some work of Morrey which assumes that the growth rate of the ${L^p}$ norm of the gradient of a function on balls is bounded by some power of the radius.References
- 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). MR 414802, DOI 10.5802/aif.507
- S. Campanato, Proprietà di una famiglia di spazi funzionali, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 18 (1964), 137–160 (Italian). MR 167862
- F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415–426. MR 131498, DOI 10.1002/cpa.3160140317
- Norman G. Meyers, Mean oscillation over cubes and Hölder continuity, Proc. Amer. Math. Soc. 15 (1964), 717–721. MR 168712, DOI 10.1090/S0002-9939-1964-0168712-3
- Charles B. Morrey Jr., On the solutions of quasi-linear elliptic partial differential equations, Trans. Amer. Math. Soc. 43 (1938), no. 1, 126–166. MR 1501936, DOI 10.1090/S0002-9947-1938-1501936-8
- S. M. Nikol′skiĭ, Approximation of functions of several variables and imbedding theorems, Die Grundlehren der mathematischen Wissenschaften, Band 205, Springer-Verlag, New York-Heidelberg, 1975. Translated from the Russian by John M. Danskin, Jr. MR 0374877, DOI 10.1007/978-3-642-65711-5 G. Stampacchia, The spaces ${L^{(p,\lambda )}},{N^{(p,\lambda )}}$ and interpolation, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 19 (1965), 293-306.
Bibliographic Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 78 (1980), 97-102
- MSC: Primary 46E35
- DOI: https://doi.org/10.1090/S0002-9939-1980-0548092-0
- MathSciNet review: 548092