2,392 research outputs found
Homogenization of a parabolic Dirichlet problem by a method of Dahlberg
Consider the linear parabolic operator in divergence form We employ a method of
Dahlberg to show that the Dirichlet problem for in the upper half
plane is well-posed for boundary data in , for any elliptic matrix of
coefficients which is periodic and satisfies a Dini-type condition. This
result allows us to treat a homogenization problem for the equation in
Lipschitz domains with -boundary data.Comment: 21 page
On fundamental harmonic analysis operators in certain Dunkl and Bessel settings
We consider several harmonic analysis operators in the multi-dimensional
context of the Dunkl Laplacian with the underlying group of reflections
isomorphic to (also negative values of the multiplicity
function are admitted). Our investigations include maximal operators,
-functions, Lusin area integrals, Riesz transforms and multipliers of
Laplace and Laplace-Stieltjes transform type. Using the general
Calder\'on-Zygmund theory we prove that these objects are bounded in weighted
spaces, , and from into weak .Comment: 26 pages. arXiv admin note: text overlap with arXiv:1011.3615 by
other author
Calder\'on-Zygmund operators in the Bessel setting for all possible type indices
In this paper we adapt the technique developed in [17] to show that many
harmonic analysis operators in the Bessel setting, including maximal operators,
Littlewood-Paley-Stein type square functions, multipliers of Laplace or
Laplace-Stieltjes transform type and Riesz transforms are, or can be viewed as,
Calder\'on-Zygmund operators for all possible values of type parameter
in this context. This extends the results obtained recently in [7],
which are valid only for a restricted range of .Comment: 12 page
Bounds for partial derivatives: necessity of UMD and sharp constants
We prove the necessity of the UMD condition, with a quantitative estimate of
the UMD constant, for any inequality in a family of bounds between
different partial derivatives of . In particular, we show that the estimate
characterizes the UMD property,
and the best constant is equal to one half of the UMD constant. This
precise value of seems to be new even for scalar-valued functions.Comment: v2: corrected typo in the reference
Calder\'on-Zygmund operators in the Bessel setting
We study several fundamental operators in harmonic analysis related to Bessel
operators, including maximal operators related to heat and Poisson semigroups,
Littlewood-Paley-Stein square functions, multipliers of Laplace transform type
and Riesz transforms. We show that these are (vector-valued) Calder\'on-Zygmund
operators in the sense of the associated space of homogeneous type, and hence
their mapping properties follow from the general theory.Comment: 21 page
UMD Banach spaces and the maximal regularity for the square root of several operators
In this paper we prove that the maximal -regularity property on the
interval , , for Cauchy problems associated with the square root of
Hermite, Bessel or Laguerre type operators on
characterizes the UMD property for the Banach space .Comment: 23 pages. To appear in Semigroup Foru
Characterization of Banach valued BMO functions and UMD Banach spaces by using Bessel convolutions
In this paper we consider the space of bounded mean
oscillations and odd functions on taking values in a UMD Banach
space . The functions in are characterized by Carleson
type conditions involving Bessel convolutions and -radonifying norms.
Also we prove that the UMD Banach spaces are the unique Banach spaces for which
certain -radonifying Carleson inequalities for Bessel-Poisson integrals
of functions hold.Comment: 29 page
Solvability of the Dirichlet, Neumann and the regularity problems for parabolic equations with H\"older continuous coefficients
We establish the -solvability of Dirichlet, Neumann and regularity
problems for divergence-form heat (or diffusion) equations with
H\"older-continuous diffusion coefficients, on bounded Lipschitz domains in
. This is achieved through the demonstration of invertibility of
the relevant layer-potentials which is in turn based on Fredholm theory and a
new systematic approach which yields suitable parabolic Rellich-type estimates
Transference of local to global maximal estimates for dispersive partial differential equations
In this paper we give an elementary proof for transference of local to global
maximal estimates for dispersive PDEs. This is done by transferring local
estimates for certain oscillatory integrals with rough phase functions, to the
corresponding global estimates. The elementary feature of our approach is that
it entirely avoids the use of the wave packet techniques which are quite common
in this context, and instead is based on scalings and classical oscillatory
integral estimates.Comment: 10 page
Oscillation of generalized differences of H\"older and Zygmund functions
In this paper we analyze the oscillation of functions having derivatives in
the H\"older or Zygmund class in terms of generalized differences and prove
that its growth is governed by a version of the classical Kolmogorov's Law of
the Iterated Logarithm. A better behavior is obtained for functions in the
Lipschitz class via an interesting connection with Calder\'on-Zygmund
operators.Comment: 16 page
- …