17,531,441 research outputs found
Renormings of
We investigate the best order of smoothness of . We prove in
particular that there exists a -smooth bump function on if
and only if and are both even integers and is a multiple of .Comment: 18 pages; AMS-Te
L^p-tauberian theorems and L^p-rates for energy decay
We prove -analogues of the classical tauberian theorem of Ingham and
Karamata, and its variations giving rates of decay. These results are applied
to derive -decay of operator families arising in the study of the decay of
energy for damped wave equations and local energy for wave equations in
exterior domains. By constructing some examples of critical behaviour we show
that the -rates of decay obtained in this way are best possible under our
assumptions.Comment: Minor corrections have been mad
On -- trace inequalities
We give necessary and sufficient conditions in order that inequalities of the
type hold for a class of integral operators with nonnegative kernels, and measures and
on , in the case where and .
An important model is provided by the dyadic integral operator with kernel
, where
is the family of all dyadic cubes in , and are
arbitrary nonnegative constants associated with .
The corresponding continuous versions are deduced from their dyadic
counterparts. In particular, we show that, for the convolution operator with positive radially decreasing kernel , the trace
inequality holds if and only if , where
. Here is a nonlinear Wolff
potential defined by and
. Analogous inequalities for
were characterized earlier by the authors using a different method
which is not applicable when
Stochastic maximal -regularity
In this article we prove a maximal -regularity result for stochastic
convolutions, which extends Krylov's basic mixed -inequality for the
Laplace operator on to large classes of elliptic operators,
both on and on bounded domains in with
various boundary conditions. Our method of proof is based on McIntosh's
-functional calculus, -boundedness techniques and sharp
-square function estimates for stochastic integrals in -spaces.
Under an additional invertibility assumption on , a maximal space--time
-regularity result is obtained as well.Comment: Published in at http://dx.doi.org/10.1214/10-AOP626 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Multivariate p-dic L-function
We construct multivariate p-adic L-function in the p-adic number fild by
using Washington method.Comment: 9 page
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