257 research outputs found
Smoothing estimates for non-dispersive equations
This paper describes an approach to global smoothing problems for
non-dispersive equations based on ideas of comparison principle and canonical
transformation established in authors' previous paper, where dispersive
equations were treated. For operators of order satisfying the
dispersiveness condition for , the global
smoothing estimate is well-known,
while it is also known to fail for non-dispersive operators. For the case when
the dispersiveness breaks, we suggest the estimate in the form which is
equivalent to the usual estimate in the dispersive case and is also invariant
under canonical transformations for the operator . We show that this
estimate and its variants do continue to hold for a variety of non-dispersive
operators , where may become zero on some set.
Moreover, other types of such estimates, and the case of time-dependent
equations are also discussed.Comment: 24 pages; the paper is to appear in Math. Ann. arXiv admin note:
substantial text overlap with arXiv:math/061227
Trace theorems: critical cases and best constants
The purpose of this paper is to present the critical cases of the trace
theorems for the restriction of functions to closed surfaces, and to give the
asymptotics for the norms of the traces under dilations of the surface. We also
discuss the best constants for them.Comment: 11 pages. arXiv admin note: text overlap with arXiv:math/061227
The inclusion relation between Sobolev and modulation spaces
The inclusion relations between the -Sobolev spaces and the modulation
spaces is determined explicitly. As an application, mapping properties of
unimodular Fourier multiplier between -Sobolev spaces
and modulation spaces are discussed.Comment: 21 page
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
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