INVESTIGADORES
OMBROSI Sheldy Javier
artículos
Título:
Weak type estimates for singular integrals related to a dual problem of Muckenhoupt and Wheeden
Autor/es:
A. LERNER, S. OMBROSI Y C. PÉREZ
Revista:
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
Editorial:
BIRKHAUSER BOSTON INC
Referencias:
Año: 2009 vol. 15 p. 394 - 394
ISSN:
1069-5869
Resumen:
A well-known open problem of Muckenhoupt¨CWheeden says that any Calder¨®n¨CZygmund singular integral operator T is of weak type (1, 1) with respect to a couple of weights (w,Mw). In this paper, we consider a somewhat ¡°dual¡± problem: sup sup a couple of weights (w,Mw). In this paper, we consider a somewhat ¡°dual¡± problem: sup sup T is of weak type (1, 1) with respect to a couple of weights (w,Mw). In this paper, we consider a somewhat ¡°dual¡± problem: sup sup (w,Mw). In this paper, we consider a somewhat ¡°dual¡± problem: sup ¦Ë>00 ¦Ëwx ¡Ê Rn : |Tf (x)|¡Ê Rn : |Tf (x)| Mw >¦Ë ¡Ü c Rn |f |dx. ¡Ü c Rn |f |dx. We prove a weaker version of this inequality withM3w instead ofMw. Also we study a related question about the behavior of the constant in terms of the A1 characteristic of w. of w. a related question about the behavior of the constant in terms of the A1 characteristic of w. of w. M3w instead ofMw. Also we study a related question about the behavior of the constant in terms of the A1 characteristic of w. of w. A1 characteristic of w.w.