Weighted Sobolev inequalities on domains satisfying the chain condition

Chua, Seng-Kee

doi:10.1090/S0002-9939-1993-1140667-2

Weighted Sobolev inequalities on domains satisfying the chain condition
HTML articles powered by AMS MathViewer

by Seng-Kee Chua

Proc. Amer. Math. Soc. 117 (1993), 449-457

DOI: https://doi.org/10.1090/S0002-9939-1993-1140667-2

PDF | Request permission

Abstract:

By similar methods of Iwaniec and Nolder (Hardy-Littlewood inequality for quasiregular mappings in certain domains in ${\mathbb {R}^n}$, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985)), we obtain weighted Sobolev inequalities on domains satisfying the Boman chain condition.

References

B. Bojarski, Remarks on Sobolev imbedding inequalities, Complex analysis, Joensuu 1987, Lecture Notes in Math., vol. 1351, Springer, Berlin, 1988, pp. 52–68. MR 982072, DOI 10.1007/BFb0081242

Poincaré inequalities for a class of non

weights

Seng-Kee Chua, Extension theorems on weighted Sobolev spaces, Indiana Univ. Math. J. 41 (1992), no. 4, 1027–1076. MR 1206339, DOI 10.1512/iumj.1992.41.41053

Extension theorems on weighted Sobolev spaces

Extension and restriction theorems on weighted Sobolev spaces

Filippo Chiarenza and Michele Frasca, A note on a weighted Sobolev inequality, Proc. Amer. Math. Soc. 93 (1985), no. 4, 703–704. MR 776206, DOI 10.1090/S0002-9939-1985-0776206-0
W. D. Evans and D. J. Harris, Sobolev embeddings for generalized ridged domains, Proc. London Math. Soc. (3) 54 (1987), no. 1, 141–175. MR 872254, DOI 10.1112/plms/s3-54.1.141
Eugene B. Fabes, Carlos E. Kenig, and Raul P. Serapioni, The local regularity of solutions of degenerate elliptic equations, Comm. Partial Differential Equations 7 (1982), no. 1, 77–116. MR 643158, DOI 10.1080/03605308208820218
Ritva Hurri, Poincaré domains in $\textbf {R}^n$, Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes 71 (1988), 42. MR 978019
Ritva Hurri, The weighted Poincaré inequalities, Math. Scand. 67 (1990), no. 1, 145–160. MR 1081294, DOI 10.7146/math.scand.a-12325
T. Iwaniec and C. A. Nolder, Hardy-Littlewood inequality for quasiregular mappings in certain domains in $\textbf {R}^n$, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985), 267–282. MR 802488, DOI 10.5186/aasfm.1985.1030
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
Peter W. Jones, Quasiconformal mappings and extendability of functions in Sobolev spaces, Acta Math. 147 (1981), no. 1-2, 71–88. MR 631089, DOI 10.1007/BF02392869
O. Martio and J. Sarvas, Injectivity theorems in plane and space, Ann. Acad. Sci. Fenn. Ser. A I Math. 4 (1979), no. 2, 383–401. MR 565886, DOI 10.5186/aasfm.1978-79.0413

Weighted inequalities for fractional integrals on Euclidean and homogeneous spaces

Wayne Smith and David A. Stegenga, Hölder domains and Poincaré domains, Trans. Amer. Math. Soc. 319 (1990), no. 1, 67–100. MR 978378, DOI 10.1090/S0002-9947-1990-0978378-8
Susan G. Staples, $L^p$-averaging domains and the Poincaré inequality, Ann. Acad. Sci. Fenn. Ser. A I Math. 14 (1989), no. 1, 103–127. MR 997974, DOI 10.5186/aasfm.1989.1429
Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
Jan-Olov Strömberg and Alberto Torchinsky, Weighted Hardy spaces, Lecture Notes in Mathematics, vol. 1381, Springer-Verlag, Berlin, 1989. MR 1011673, DOI 10.1007/BFb0091154
Alberto Torchinsky, Real-variable methods in harmonic analysis, Pure and Applied Mathematics, vol. 123, Academic Press, Inc., Orlando, FL, 1986. MR 869816