7,182 research outputs found
UMD-valued square functions associated with Bessel operators in Hardy and BMO spaces
We consider Banach valued Hardy and BMO spaces in the Bessel setting. Square
functions associated with Poisson semigroups for Bessel operators are defined
by using fractional derivatives. If B is a UMD Banach space we obtain for
B-valued Hardy and BMO spaces equivalent norms involving -radonifying
operators and square functions. We also establish characterizations of UMD
Banach spaces by using Hardy and BMO-boundedness properties of g-functions
associated to Bessel-Poisson semigroup
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
UMD Banach spaces and square functions associated with heat semigroups for Schr\"odinger and Laguerre operators
In this paper we define square functions (also called Littlewood-Paley-Stein
functions) associated with heat semigroups for Schr\"odinger and Laguerre
operators acting on functions which take values in UMD Banach spaces. We extend
classical (scalar) L^p-boundedness properties for the square functions to our
Banach valued setting by using \gamma-radonifying operators. We also prove that
these L^p-boundedness properties of the square functions actually characterize
the Banach spaces having the UMD property
Characterization of UMD Banach spaces by imaginary powers of Hermite and Laguerre operators
In this paper we characterize the Banach spaces with the UMD property by
means of Lp-boundedness properties for the imaginary powers of the Hermite and
Laguerre operators. In order to do this we need to obtain pointwise
representations for the Laplace transform type multipliers associated with
Hermite and Laguerre operators.Comment: 17 page
Variable exponent Hardy spaces associated with discrete Laplacians on graphs
In this paper we develop the theory of variable exponent Hardy spaces
associated with discrete Laplacians on infinite graphs. Our Hardy spaces are
defined by square integrals, atomic and molecular decompositions. Also we study
boundedness properties of Littlewood-Paley functions, Riesz transforms, and
spectral multipliers for discrete Laplacians on variable exponent Hardy spaces
Discrete harmonic analysis associated with ultraspherical expansions
We study discrete harmonic analysis associated with ultraspherical orthogonal
functions. We establish weighted l^p-boundedness properties of maximal
operators and Littlewood-Paley g-functions defined by Poisson and heat
semigroups generated by certain difference operator. We also prove weighted
l^p-boundedness properties of transplantation operators associated to the
system of ultraspherical functions. In order to show our results we previously
establish a vector-valued local Calder\'on-Zygmund theorem in our discrete
setting
Conical square functions associated with Bessel, Laguerre and Schr\"odinger operators in UMD Banach spaces
In this paper we consider conical square functions in the Bessel, Laguerre
and Schr\"odinger settings where the functions take values in UMD Banach
spaces. Following a recent paper of Hyt\"onen, van Neerven and Portal, in order
to define our conical square functions, we use -radonifying operators.
We obtain new equivalent norms in the Lebesgue-Bochner spaces and , , in terms of
our square functions, provided that is a UMD Banach space. Our
results can be seen as Banach valued versions of known scalar results for
square functions
Solutions of Weinstein equations representable by Bessel Poisson integrals of BMO functions
We consider the Weinstein type equation on
, where , with . In
this paper we characterize the solutions of on
representable by Bessel-Poisson integrals of
BMO-functions as those ones satisfying certain Carleson properties
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