INVESTIGADORES
AIMAR Hugo Alejandro A.
artículos
Título:
On weighted inequalities for singular integrals
Autor/es:
AIMAR HUGO; FORZANI LILIANA; MARTIN-REYES FRANCISCO
Revista:
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Editorial:
AMER MATHEMATICAL SOC
Referencias:
Lugar: Providence; Año: 1997 vol. 125 p. 2057 - 2064
ISSN:
0002-9939
Resumen:
In this note we consider singular integrals associated to Calderon-Zygmund kernels. We prove that if the kernel is supported in (0;1) then theone-sided Ap condition, A−p , is a sufficient condition for the singular integralto be bounded in Lp(w), 1 < p <1, or from L1(wdx) into weak-L1(wdx) ifp = 1. This one-sided Ap condition becomes also necessary when we requirethe uniform boundedness of the singular integrals associated to the dilationsof a kernel which is not identically zero in (0;1). The two-sided version ofthis result is also obtained: Muckenhoupt's Ap condition is necessary for theuniform boundedness of the singular integrals associated to the dilations ofa general Calderon-Zygmund kernel which is not the function zero either in(−1; 0) or in (0;1).
