IAM   02674
INSTITUTO ARGENTINO DE MATEMATICA ALBERTO CALDERON
Unidad Ejecutora - UE
artículos
Título:
Characterization of the weak-type boundedness of the Hilbert transform on weighted Lorentz spaces
Autor/es:
ELONA AGORA; MARÍA JESÚS CARRO; JAVIER SORIA
Revista:
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
Editorial:
BIRKHAUSER BOSTON INC
Referencias:
Año: 2013 vol. 19 p. 712 - 712
ISSN:
1069-5869
Resumen:
We characterize the weak-type boundedness of the Hilbert transform H on weighted Lorentz spaces Λpu(w) , with p>0, in terms of some geometric conditions on the weights u and w and the weak-type boundedness of the Hardy?Littlewood maximal operator on the same spaces. Our results recover simultaneously the theory of the boundedness of H on weighted Lebesgue spaces Lp(u) and Muckenhoupt weights Ap , and the theory on classical Lorentz spaces Λp(w) and Ariño-Muckenhoupt weights Bp .