50 research outputs found
The dilation property of modulation spaces and their inclusion relation with Besov spaces
We consider the dilation property of the modulation spaces . Let
be the dilation operator, and we consider
the behavior of the operator norm with
respect to . Our result determines the best order for it, and as an
application, we establish the optimality of the inclusion relation between the
modulation spaces and Besov space, which was proved by Toft.Comment: 23 page
Sharp maximal function estimates for linear and multilinear pseudo-differential operators
In this paper, we study pointwise estimates for linear and multilinear
pseudo-differential operators with exotic symbols in terms of the
Fefferman-Stein sharp maximal function and Hardy-Littlewood type maximal
function. Especially in the multilinear case, we use a multi-sublinear variant
of the classical Hardy-Littlewood maximal function introduced by Lerner,
Ombrosi, P\'erez, Torres, and Trujillo-Gonz\'alez, which provides more
elaborate and natural weighted estimates in the multilinear setting