A note on multilinear Muckenhoupt classes for multiple weights
Tom 223 / 2014
Studia Mathematica 223 (2014), 1-18
MSC: Primary 42B35; Secondary 42B99.
DOI: 10.4064/sm223-1-1
Streszczenie
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.
