Weighted inequalities and the shape of approach regions

• Autorzy: José L. García , Javier Soria
• Języki publikacji: EN

Abstrakty

EN

We characterize geometric properties of a family of approach regions by means of analytic properties of the class of weights related to the boundedness of the maximal operator associated with this family.

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1999
• Tom: 133
• Numer: 3
• Strony: 261-274

Daty

wydano

1999

otrzymano

1998-01-19

Twórcy

autor

José L. García

• Departament de Matemàtica i Informàtica, Universitat de Vic, E-08500 Vic, Spain

autor

Javier Soria

• Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, E-08071 Barcelona, Spain

Bibliografia

• [AC] M. Andersson and H. Carlsson, Boundary convergence in non-tangential and non-admissible approach regions, Math. Scand. 70 (1992), 293-301.
• [CR] R. R. Coifman and R. Rochberg, Another characterization of BMO, Proc. Amer. Math. Soc. 79 (1980), 249-254.
• [CW] R. R. Coifman et G. Weiss, Analyse Harmonique Non-Commutative sur Certains Espaces Homogènes, Lecture Notes in Math. 242, Springer, 1971.
• [Ja] B. Jawerth, Weighted inequalities for maximal operators: linearization, localization and factorization, Amer. J. Math. 108 (1986), 361-414.
• [NS] A. Nagel and E. M. Stein, On certain maximal functions and approach regions, Adv. Math. 54 (1984), 83-106.
• [Pa] J. W. Pan, Weighted norm estimates for certain maximal operators with approach regions, in: Lecture Notes in Math. 1494, Springer, 1992, 169-175.
• [SS1] A. Sánchez-Colomer and J. Soria, Weighted norm inequalities for general maximal operators and approach regions, Math. Nachr. 172 (1995), 249-260.
• [SS2] A. Sánchez-Colomer and J. Soria, $A_p$ and approach regions, in: Fourier Analysis and Partial Differential Equations, CRC Press, 1995, 311-315.
• [ST] J. O. Strömberg and A. Torchinsky, Weighted Hardy Spaces, Lecture Notes in Math. 1381, Springer, 1989.
• [Su] J. Sueiro, On maximal functions and Poisson-Szegő integrals, Trans. Amer. Math. Soc. 298 (1986), 653-669.