1,538 research outputs found
Weighted norm inequalities, Gaussian bounds and sharp spectral multipliers
Let be a non-negative self adjoint operator acting on where
is a space of homogeneous type. Assume that generates a holomorphic
semigroup whose kernels have Gaussian upper bounds but
possess no regularity in variables and . In this article, we study
weighted -norm inequalities for spectral multipliers of . We show sharp
weighted H\"ormander-type spectral multiplier theorems follow from Gaussian
heat kernel bounds and appropriate estimates of the kernels of the
spectral multipliers. These results are applicable to spectral multipliers for
large classes of operators including Laplace operators acting on Lie groups of
polynomial growth or irregular non-doubling domains of Euclidean spaces,
elliptic operators on compact manifolds and Schr\"odinger operators with
non-negative potentials on complete Riemannian manifolds
Characterization of coorbit spaces with phase-space covers
We show that coorbit spaces can be characterized in terms of arbitrary
phase-space covers, which are families of phase-space multipliers associated
with partitions of unity. This generalizes previously known results for
time-frequency analysis to include time-scale decompositions. As a by-product,
we extend the existing results for time-frequency analysis to an irregular
setting.Comment: 31 pages. Revised version (title slightly changed). Typos fixe
Weak type operator Lipschitz and commutator estimates for commuting tuples
Let be a Lipschitz function. If is a
bounded self-adjoint operator and if are commuting bounded
self-adjoint operators such that then
where is
a constant independent of , and and
denotes the weak -norm. If
(respectively, ) are commuting bounded self-adjoint operators
such that then
\|f(X_1,\cdots,X_d)-f(Y_1,\cdots,Y_d)\|_{1,\infty}\leq
c(d)\|\nabla(f)\|_{\infty}\max_{1\leq k\leq d}\|X_k-Y_k\|_1.$
Nonharmonic analysis of boundary value problems
In this paper we develop the global symbolic calculus of pseudo-differential
operators generated by a boundary value problem for a given (not necessarily
self-adjoint or elliptic) differential operator. For this, we also establish
elements of a non-self-adjoint distribution theory and the corresponding
biorthogonal Fourier analysis. We give applications of the developed analysis
to obtain a-priori estimates for solutions of operators that are elliptic
within the constructed calculus.Comment: 54 pages, updated version, to appear in IMR
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