Best approach regions for potential spaces
HTML articles powered by AMS MathViewer
- by José A. Raposo and Javier Soria
- Proc. Amer. Math. Soc. 125 (1997), 1105-1109
- DOI: https://doi.org/10.1090/S0002-9939-97-03680-0
- PDF | Request permission
Abstract:
We characterize the approach regions so that the non-tangential maximal function is of weak-type on potential spaces, for which we use a simple argument involving Carleson measure estimates.References
- Mats Andersson and Hasse Carlsson, Boundary convergence in non-nontangential and nonadmissible approach regions, Math. Scand. 70 (1992), no. 2, 293–301. MR 1189981, DOI 10.7146/math.scand.a-12403
- María J. Carro and Javier Soria, Tent spaces over general approach regions and pointwise estimates, Pacific J. Math. 163 (1994), no. 2, 217–235. MR 1262295, DOI 10.2140/pjm.1994.163.217
- J.E. Littlewood, On a theorem of Fatou, J. London Math. Soc. 2 (1927), 172 –176.
- Alexander Nagel, Walter Rudin, and Joel H. Shapiro, Tangential boundary behavior of functions in Dirichlet-type spaces, Ann. of Math. (2) 116 (1982), no. 2, 331–360. MR 672838, DOI 10.2307/2007064
- Alexander Nagel and Elias M. Stein, On certain maximal functions and approach regions, Adv. in Math. 54 (1984), no. 1, 83–106. MR 761764, DOI 10.1016/0001-8708(84)90038-0
- Ascensión Sánchez-Colomer and Javier Soria, Weighted norm inequalities for general maximal operators and approach regions, Math. Nachr. 172 (1995), 249–260. MR 1330633, DOI 10.1002/mana.19951720118
- Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
Bibliographic Information
- José A. Raposo
- Affiliation: Departamento Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, 08071 Barcelona, Spain
- Email: raposo@cerber.mat.ub.es
- Javier Soria
- Affiliation: Departamento Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, 08071 Barcelona, Spain
- Email: soria@cerber.mat.ub.es
- Received by editor(s): August 9, 1994
- Received by editor(s) in revised form: October 4, 1995
- Additional Notes: This work has been partially supported by DGICYT PB94–0879
- Communicated by: J. Marshall Ash
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1105-1109
- MSC (1991): Primary 42B25, 42B20
- DOI: https://doi.org/10.1090/S0002-9939-97-03680-0
- MathSciNet review: 1363181