Some weighted norm inequalities for a one-sided version of $g_{\lambda }^*$

L. de Rosa¹ ; C. Segovia²

¹ Juan José Olleros 2969 8 B 1426 Buenos Aires, Argentina
² Departamento de Matemática Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires 1428 Buenos Aires, Argentina and Instituto Argentino de Matemática CONICET Saavedra 15 3er Piso 1083 Buenos Aires, Argentina

Studia Mathematica, Tome 176 (2006) no. 1, pp. 21-36

Résumé

We study the boundedness of the one-sided operator $g_{\lambda ,\varphi }^+$ between the weighted spaces $L^p(M^{-}w)$ and $L^p(w)$ for every weight $w.$ If $\lambda = 2/p$ whenever $1 p 2,$ and in the case $p=1$ for $\lambda >2,$ we prove the weak type of $g_{\lambda ,\varphi }^+.$ For every $\lambda >1$ and $p=2,$ or $\lambda > 2/p$ and $1 p 2,$ the boundedness of this operator is obtained. For $p>2$ and $\lambda >1,$ we obtain the boundedness of $g_{\lambda ,\varphi }^+$ from $L^p((M^{-})^{[p/2]+1} w)$ to $L^p(w),$ where $(M^{-})^{k}$ denotes the operator $M^{-}$ iterated $k$ times.

Détail

DOI : 10.4064/sm176-1-2

Keywords: study boundedness one sided operator lambda varphi between weighted spaces every weight lambda whenever lambda prove weak type lambda varphi every lambda lambda boundedness operator obtained lambda obtain boundedness lambda varphi where denotes operator iterated times