A note on multilinear Muckenhoupt classes for multiple weights

Songqing Chen ¹   ; Huoxiong Wu ²   ; Qingying Xue ³

¹ School of Mathematical Sciences Xiamen University Xiamen, Fujian 361005, China and School of Economics Shanghai University of Finance and Economics Shanghai 240033, China
² School of Mathematical Sciences Xiamen University Xiamen, Fujian 361005, China
³ School of Mathematical Sciences Beijing Normal University Beijing 100875, China

Studia Mathematica, Tome 223 (2014) no. 1, pp. 1-18

Résumé

This paper is devoted to investigating the properties of multilinear $A_{\vec{P}}$ conditions and $A_{(\vec{P},q)}$ conditions, which are suitable for the study of multilinear operators on Lebesgue spaces. Some monotonicity properties of $A_{\vec{P}}$ and $A_{(\vec{P},q)}$ classes with respect to $\vec{P}$ and $q$ are given, although these classes are not in general monotone with respect to the natural partial order. Equivalent characterizations of multilinear $A_{(\vec{P},q)}$ classes in terms of the linear $A_p$ classes are established. These results essentially improve and extend the previous results.

Détail

DOI : 10.4064/sm223-1-1

Keywords: paper devoted investigating properties multilinear vec conditions vec conditions which suitable study multilinear operators lebesgue spaces monotonicity properties vec vec classes respect vec given although these classes general monotone respect natural partial order equivalent characterizations multilinear vec classes terms linear classes established these results essentially improve extend previous results