Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-24T12:06:37.938Z Has data issue: false hasContentIssue false
  • English
  • Français

On q-Carleson Measures for Spaces of M-Harmonic Functions

Published online by Cambridge University Press:  20 November 2018

Carme Cascante  and
Joaquin M. Ortega
Carme Cascante
Affiliation:
Departament de Matemàtica Aplicada i Anàlisi, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08071 Barcelona, Spain e-mail: [email protected], e-mail: [email protected]
Joaquin M. Ortega
Affiliation:
Departament de Matemàtica Aplicada i Anàlisi, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08071 Barcelona, Spain e-mail: [email protected], e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we study the q-Carleson measures for a space of M-harmonic potentials in the unit ball of Cn, when q < p. We obtain some computable sufficient conditions, and study the relations among them.

Keywords

32A3531C15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 4 , 01 August 1997 , pp. 653 - 674
Copyright
Copyright © Canadian Mathematical Society 1997

References

[Ad] Adams, D.R., Lectures on Lp-potential theory. Umea Univ. Reports 2(1981), 417–451.Google Scholar
[AhCo] Ahern, P. and Cohn, W., Exceptional sets for Hardy-Sobolev functions, p > 1, Indiana Univ. Math. J. 38(1989), 417–451.+1,+Indiana+Univ.+Math.+J.+38(1989),+417–451.>Google Scholar
[AhNa] Ahern, P. and Nagel, A., Strong Lp-estimates for maximal functions with respect to singular measures with applications to exceptional sets. Duke Math. J. 53(1986), 359–393.Google Scholar
[Ca] Carleson, L., Interpolation by bounded analytic functions and the corona theorem. Ann. of Math. 76(1962), 547–559.Google Scholar
[CaOr1] Cascante, C. and Ortega, J.M., Carleson measures on spaces of Hardy-Sobolev type. Canad. Math. J. 47(1995), 1177–1200.Google Scholar
[CaOr2] Cascante, C., Tangential-exceptional sets for Hardy-Sobolev spaces. Illinois J. Math. 39(1995), 68–85.Google Scholar
[CoVe1] Cohn, W.S. and Verbistky, I.E., On the trace inequalities for Hardy-Sobolev functions in the unit ball of Cn. Indiana Univ. Math. J. 43(1994), 1079–1097.Google Scholar
[CoVe2] Cohn, W.S., Non-linear potential theory on the ball, with applications to exceptional and boundary interpolation sets. Michigan Math. J. 42(1995), 79–97.Google Scholar
[CoMeSt] Coifmann, R.R., Meyer, Y. and Stein, E.M., Some new function spaces and their applications to harmonic analysis. J. Funct. Anal. 62(1985), 304–335.Google Scholar
[HeWo] Hedberg, L.I. and Wolff, Th. H., Thin sets in nonlinear potential theory. Ann. Inst. Fourier (Grenoble) 33(1983), 161–187.Google Scholar
[Lu1] Luecking, D.H., Embedding derivatives of Hardy spaces into Lebesgue spaces. Proc. LondonMath. Soc. 3(1991), 595–619..Google Scholar
[Lu2] Luecking, D.H., Representation and duality in weighted spaces of analytic functions. Indiana Univ. Math. J. 34(1985), 319–336.Google Scholar
[Ma] Maz’ya, V.G., Sobolev spaces, Springer-Verlag, 1985.Google Scholar
[MaKh] Maz’ya, V. G. and Khavin, V.P., Non-linear potential theory. RussianMath. Surveys 27(1972), 71–148.Google Scholar
[MaNe] Maz’ya, V. G. and Y.Netrusov, Some counterexamples for the theory of Sobolev spaces on bad domains. Potential Analysis 4(1995), 47–65.Google Scholar
[NaRuSh] Nagel, A., Rudin, W. and Shapiro, J.H., Tangential boundary behavior of functions in Dirichlet-type spaces. Ann. of Math. 116(1982), 331–360.Google Scholar
[Ru] Rudin, W., Function theory in the unit ball, Springer Verlag, 1980.Google Scholar
[St] Stegenga, D.A., Multipliers of the Dirichlet space. Illinois J. Math. 24(1980), 113–139.Google Scholar
[Su] Sueiro, J., Tangential boundary limits and exceptional sets for holomorphic functions in Dirichlet-type spaces. Math. Ann. 286(1990), 661–678.Google Scholar
[Ve] Verbitsky, I.E., Weighted norm inequalities for maximal operators and Pisier's theorem on factorization. through Lp∞, Integral Equations Operator Theory 15(1992), 124–153.Google Scholar
[Yo] Yoo, Y.J., Area integral associated with singular measures on the unit sphere on Cn. Rocky Mountain J. Math. 25(1995), 815–825.Google Scholar