A condition implying boundedness and VMO for a function f

 Access to full text

 Full (PDF)

1. [1] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, New York, 1988. Zbl0647.46057
2. [2] C. Bennett, R. DeVore and R. Sharpley, Weak-$L^{\infty }$ and BMO, Ann. of Math. 113 (1981), 601-611. 
3. [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. Zbl0582.30016
4. [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. Zbl0816.35045
5. [5] S. Campanato, Proprietà di hölderianità di alcune classi di funzioni, Ann. Scuola Norm. Sup. Pisa 17 (1963), 175-188. 
6. [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. [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. [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. Zbl0818.35023
9. [9] G. Di Fazio, $L^p$ estimates for divergence form elliptic equations with discontinuous coefficients, preprint, Università di Catania. 
10. [10] M. Franciosi, Weighted rearrangements and higher integrability results, Studia Math. 92 (1989), 131-138. Zbl0677.42021
11. [11] M. Franciosi, Higher integrability results and Hölder continuity, J. Math. Anal. Appl. 150 (1990), 161-165. Zbl0732.42013
12. [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. [13] C. Herz, The Hardy-Littlewood maximal theorem, in: Symposium on Harmonic Analysis, University of Warwick, 1968. 
14. [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. Zbl0505.30011
15. [15] F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (1961), 415-426. Zbl0102.04302
16. [16] A. Korenovskii, One refinement of the Gurov-Reshetnyak inequality, preprint, Université de Toulon et du Var. Zbl0920.26014
17. [17] D. Sarason, Functions of vanishing mean oscillation, Trans. Amer. Math. Soc. 207 (1975), 391-405. Zbl0319.42006
18. [18] S. Spanne, Some function spaces defined using the mean oscillation over cubes, Ann. Scuola Norm. Sup. Pisa 19 (1965), 593-608. Zbl0199.44303