naa a22 4500 510810535 CHVBK 20180411083440.0 cr unu---uuuuu 180411e20130701xx s 000 0 eng 10.1007/s12220-011-9290-0 doi (NATIONALLICENCE)springer-10.1007/s12220-011-9290-0 Lerner Andrei Department of Mathematics, Bar-Ilan University, 52900, Ramat Gan, Israel aut Mixed A p - A r Inequalities for Classical Singular Integrals and Littlewood-Paley Operators [Elektronische Daten] [Andrei Lerner] We prove mixed A p -A r inequalities for several basic singular integrals, Littlewood-Paley operators, and the vector-valued maximal function. Our key point is that r can be taken arbitrarily big. Hence, such inequalities are close in spirit to those obtained recently in the works by T.Hytönen and C.Pérez, and M.Lacey. On one hand, the "A p -A ∞” constant in these works involves two independent suprema. On the other hand, the "A p -A r ” constant in our estimates involves a joint supremum, but of a bigger expression. We show in simple examples that both such constants are incomparable. This leads to a natural conjecture that the estimates of both types can be further improved. Mathematica Josephina, Inc., 2011 Sharp weighted inequalities nationallicence A p weights nationallicence A ∞ weights nationallicence Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/3(2013-07-01), 1343-1354 1050-6926 23:3<1343 2013 23 12220 https://doi.org/10.1007/s12220-011-9290-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-011-9290-0 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Lerner Andrei Department of Mathematics, Bar-Ilan University, 52900, Ramat Gan, Israel aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer US; http://www.springer-ny.com 23/3(2013-07-01), 1343-1354 1050-6926 23:3<1343 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer