A note on weighted inequalities for a one-sided maximal operator in  R n .

María Lorente ^[1] ; Francisco J. Martín Reyes ^[1]
1. [1] Universidad de Málaga
  
  Universidad de Málaga
  
  Málaga, España
Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 58, Nº. 2, 2017, págs. 253-258
Idioma: inglés
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Resumen
- We introduce a new dyadic one-sided maximal operator M+⋯+d in Rn that allows us to obtain good weights for the Lp-boundedness of a one-sided maximal operator N+⋯+ in Rn, which is equivalent to the classical one-sided Hardy–Littlewood maximal operator in the case n=1, but not in the case n>1. In order to do this, we characterize the good pairs of weights for the weak and strong type inequalities for M+⋯+d and we use a Fefferman–Stein type inequality which gives that, in a certain sense, M+⋯+d controls N+⋯+.