The equivalence of various Lipschitz conditions on the weighted mean oscillation of a function
HTML articles powered by AMS MathViewer
- by Edward P. Lotkowski and Richard L. Wheeden PDF
- Proc. Amer. Math. Soc. 61 (1976), 323-328 Request permission
Abstract:
The main result establishes the equivalence of various Lipschitz-like conditions on the weighted mean oscillation over cubes of a function. Previously known results are obtained as special cases.References
- S. Campanato, Proprietà di hölderianità di alcune classi di funzioni, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 17 (1963), 175–188 (Italian). MR 156188 J.-G. Cuerva, Weighted ${H^p}$ spaces, Ph.D. dissertation, Washington Univ., St. Louis, Mo., 1975.
- 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 E. P. Lotkowski, Lipschitz spaces with weights, Ph.D. dissertation, Rutgers Univ., New Brunswick, N.J., 1975.
- 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
- Benjamin Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207–226. MR 293384, DOI 10.1090/S0002-9947-1972-0293384-6
- Benjamin Muckenhoupt and Richard L. Wheeden, Weighted bounded mean oscillation and the Hilbert transform, Studia Math. 54 (1975/76), no. 3, 221–237. MR 399741, DOI 10.4064/sm-54-3-221-237
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 61 (1976), 323-328
- MSC: Primary 26A16
- DOI: https://doi.org/10.1090/S0002-9939-1976-0427552-6
- MathSciNet review: 0427552