caa a22 4500 469043199 CHVBK 20180323132816.0 cr unu---uuuuu 170328e19920101xx s 000 0 eng 10.1007/BF01193770 doi (NATIONALLICENCE)springer-10.1007/BF01193770 Verbitsky I. Institute of Geophysics and Geology, Academy of Sciences of SSR Moldova, 277028, Kishinev, USSR aut Weighted norm inequalities for maximal operators and Pisier's theorem on factorization through Lp∞ [Elektronische Daten] [I. Verbitsky] It is proved that the inequality $$\int {(M_\alpha f)} ^q d\omega \leqslant C(\int {\left| f \right|^p dx} )^{q/p}$$ for the fractional maximal operator $$M_\alpha f(x) \approx \begin{array}{*{20}c} {\sup } \\ {x \in Q} \\ \end{array} \left| Q \right|^{\alpha /n - 1} \int_Q {\left| f \right|dx'} (x \in R^n )$$ holds for all f∈Lp if and only if $$\begin{array}{*{20}c} {\sup } \\ {x \in Q} \\ \end{array} (\left| Q \right|_\omega /\left| Q \right|^{1 - \alpha p/n} ) \in L^{q/ (p - q)} (\omega )$$ provided 0<q<p<∞, 1<p<∞, 0<α<n/p. Similar two-weight inequalities, as well as some extensions, including Riesz potentials, are also given. (The case p≤q has been treated by E.T. Sawyer [18], [19].) The proofs make use of a result of G. Pisier [17] related to the theory of factorization of operators through (weak) Lp-spaces. Birkhäuser Verlag, 1992 Integral Equations and Operator Theory Birkhäuser-Verlag 15/1(1992-01-01), 124-153 0378-620X 15:1<124 1992 15 20 https://doi.org/10.1007/BF01193770 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01193770 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Verbitsky I. Institute of Geophysics and Geology, Academy of Sciences of SSR Moldova, 277028, Kishinev, USSR aut NATIONALLICENCE 773 0- Integral Equations and Operator Theory Birkhäuser-Verlag 15/1(1992-01-01), 124-153 0378-620X 15:1<124 1992 15 20 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer