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1997 | 123 | 2 | 109-116
Tytuł artykułu

A condition implying boundedness and VMO for a function f

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EN
Abstrakty
EN
Some boundedness and VMO results are proved for a function f integrable on a cube $Q_0$, starting from an integral bound.
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Twórcy
  • DIIMA, Università di Salerno, Via S. Allende, Baronissi, Italy
Bibliografia
  • [1] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, New York, 1988.
  • [2] C. Bennett, R. DeVore and R. Sharpley, Weak-$L^∞$ and BMO, Ann. of Math. 113 (1981), 601-611.
  • [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.
  • [4] M. Bramanti and M. C. Cerutti, $W^1,2_p$ solvability for the Cauchy-Dirichlet problem for parabolic equations with VMO coefficients, Comm. Partial Differential Equations 18 (1993), 1735-1763.
  • [5] S. Campanato, Proprietà di hölderianità di alcune classi di funzioni, Ann. Scuola Norm. Sup. Pisa 17 (1963), 175-188.
  • [6] F. Chiarenza, M. Franciosi and M. Frasca, $L^p$ estimates for linear elliptic systems with discontinuous coefficients, Rend. Accad. Naz. Lincei 5 (1994), 27-32.
  • [7] F. Chiarenza, M. Frasca and P. Longo, Interior $W^2,p$ estimates for non divergence elliptic equations with discontinuous coefficients, Ricerche Mat. 40 (1991), 149-168.
  • [8] F. Chiarenza, M. Frasca and P. Longo, $W^2,p$-solvability of the Dirichlet problem for nondivergence elliptic equations with VMO coefficients, Trans. Amer. Math. Soc. 336 (1993), 841-853.
  • [9] G. Di Fazio, $L^p$ estimates for divergence form elliptic equations with discontinuous coefficients, preprint, Università di Catania.
  • [10] M. Franciosi, Weighted rearrangements and higher integrability results, Studia Math. 92 (1989), 131-138.
  • [11] M. Franciosi, Higher integrability results and Hölder continuity, J. Math. Anal. Appl. 150 (1990), 161-165.
  • [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).
  • [13] C. Herz, The Hardy-Littlewood maximal theorem, in: Symposium on Harmonic Analysis, University of Warwick, 1968.
  • [14] T. Iwaniec, On $L^p$-integrability in p.d.e. and quasiregular mappings for large exponents, Ann. Acad. Sci. Fenn. Ser. AI Math. 7 (1982), 301-322.
  • [15] F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415-426.
  • [16] A. Korenovskii, One refinement of the Gurov-Reshetnyak inequality, preprint, Université de Toulon et du Var.
  • [17] D. Sarason, Functions of vanishing mean oscillation, Trans. Amer. Math. Soc. 207 (1975), 391-405.
  • [18] S. Spanne, Some function spaces defined using the mean oscillation over cubes, Ann. Scuola Norm. Sup. Pisa 19 (1965), 593-608.
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Bibliografia
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