Two weighted inequalities for convolution maximal operators

• Autores: Ana Lucía Bernardis , Francisco Javier Martín Reyes
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 46, Nº 1, 2002, págs. 119-138
• Idioma: inglés
• DOI: 10.5565/publmat_46102_07
• Títulos paralelos:
  • Dos desigualdades ponderadas para operadores maximales de convolución
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• Resumen

  • Let $\varphi\colon \mathbb{R} \to [0,\infty)$ an integrable function such that $\varphi\chi_{(-\infty,0)} = 0$ and $\varphi$ is decreasing in $(0,\infty)$. Let $\tau_h f(x) = f(x-h)$, with $h\in \mathbb{R} \setminus \{0\}$ and $f_R(x) = \frac{1}{R}f(\frac{x}{R})$, with $R>0$. In this paper we characterize the pair of weights $(u,v)$ such that the operators $M_{\tau_h\varphi}f(x) = \sup_{R>0}|f|\ast [\tau_h\varphi]_R(x)$ are of weak type $(p,p)$ with respect to $(u,v)$, $1 < p < \infty$.