Some boundedness and VMO results are proved for a function f integrable on a cube , starting from an integral bound.
@article{bwmeta1.element.bwnjournal-article-smv123i2p109bwm, author = {Michelangelo Franciosi}, title = {A condition implying boundedness and VMO for a function f}, journal = {Studia Mathematica}, volume = {122}, year = {1997}, pages = {109-116}, zbl = {0874.26011}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv123i2p109bwm} }
Franciosi, Michelangelo. A condition implying boundedness and VMO for a function f. Studia Mathematica, Tome 122 (1997) pp. 109-116. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv123i2p109bwm/
[00000] [1] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, New York, 1988. | Zbl 0647.46057
[00001] [2] C. Bennett, R. DeVore and R. Sharpley, Weak- and BMO, Ann. of Math. 113 (1981), 601-611.
[00002] [3] B. Bojarski, Remarks on the stability of reverse Hölder inequalities and quasiconformal mappings, Ann. Acad. Sci. Fenn. Ser. AI Math. 10 (1985), 89-94. | Zbl 0582.30016
[00003] [4] M. Bramanti and M. C. Cerutti, solvability for the Cauchy-Dirichlet problem for parabolic equations with VMO coefficients, Comm. Partial Differential Equations 18 (1993), 1735-1763. | Zbl 0816.35045
[00004] [5] S. Campanato, Proprietà di hölderianità di alcune classi di funzioni, Ann. Scuola Norm. Sup. Pisa 17 (1963), 175-188.
[00005] [6] F. Chiarenza, M. Franciosi and M. Frasca, estimates for linear elliptic systems with discontinuous coefficients, Rend. Accad. Naz. Lincei 5 (1994), 27-32.
[00006] [7] F. Chiarenza, M. Frasca and P. Longo, Interior estimates for non divergence elliptic equations with discontinuous coefficients, Ricerche Mat. 40 (1991), 149-168.
[00007] [8] F. Chiarenza, M. Frasca and P. Longo, -solvability of the Dirichlet problem for nondivergence elliptic equations with VMO coefficients, Trans. Amer. Math. Soc. 336 (1993), 841-853. | Zbl 0818.35023
[00008] [9] G. Di Fazio, estimates for divergence form elliptic equations with discontinuous coefficients, preprint, Università di Catania.
[00009] [10] M. Franciosi, Weighted rearrangements and higher integrability results, Studia Math. 92 (1989), 131-138. | Zbl 0677.42021
[00010] [11] M. Franciosi, Higher integrability results and Hölder continuity, J. Math. Anal. Appl. 150 (1990), 161-165. | Zbl 0732.42013
[00011] [12] L. G. Gurov and G. Yu. Reshetnyak, On an analogue of the concept of function of bounded mean oscillation, Sibirsk. Mat. Zh. 17 (1976), 540-546 (in Russian).
[00012] [13] C. Herz, The Hardy-Littlewood maximal theorem, in: Symposium on Harmonic Analysis, University of Warwick, 1968.
[00013] [14] T. Iwaniec, On -integrability in p.d.e. and quasiregular mappings for large exponents, Ann. Acad. Sci. Fenn. Ser. AI Math. 7 (1982), 301-322. | Zbl 0505.30011
[00014] [15] F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415-426. | Zbl 0102.04302
[00015] [16] A. Korenovskii, One refinement of the Gurov-Reshetnyak inequality, preprint, Université de Toulon et du Var. | Zbl 0920.26014
[00016] [17] D. Sarason, Functions of vanishing mean oscillation, Trans. Amer. Math. Soc. 207 (1975), 391-405. | Zbl 0319.42006
[00017] [18] S. Spanne, Some function spaces defined using the mean oscillation over cubes, Ann. Scuola Norm. Sup. Pisa 19 (1965), 593-608. | Zbl 0199.44303