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 - 403
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.