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1.
2.
We prove Lp boundedness for the maximal operator of the heat semigroup associated to the Laguerre functions, , when the parameter α is greater than -1. Namely, the maximal operator is of strong type (p,p) if p>1 and , when -1<α<0. If α?0 there is strong type for 1<p?∞. The behavior at the end points is studied in detail. 相似文献
3.
Periodization and sampling operators are defined, and the Fourier transform of periodization is uniform sampling in a well-defined
sense. Implementing this point of view, Poisson Summation Formulas are proved in several spaces including integrable functions
of bounded variation (where the result is known) and elements of mixed norm spaces. These Poisson Summation Formulas can be
used to prove corresponding sampling theorems.
The sampling operators used to understand and prove the aforementioned Poisson Summation Formulas lead to the introduction
of spaces of continuous linear operators which commute with integer translations. Operators L of this type are appropriately
called sampling multipliers. For a given function f, they give rise to new sampling formulas, whose sampling coefficients
are of the form Lf. In practice, Lf can be used to model noisy data or data where point values are not available. By representation
theorems of the second named author, some of these operator spaces are proved to be mixed norm spaces.
The approach and results of this paper were developed in the context of Duffin and Schaeffer’s theory of frames. In particular,
sampling multipliers L are related to the Bessel map used by Duffin and Schaeffer in their definition of the frame operator.
The first named author was supported in part by AFOSR contract F49620-96-1-0193.
The second named author was supported by the Cusanuswerk. 相似文献
4.
Jorge J. Betancor 《Rendiconti del Circolo Matematico di Palermo》1999,48(1):51-64
In this paper we characterize weak type (1,1) inequalities for Hankel convolution operators by means of discrete methods.
Partially supported by DGICYT Grant PB 94-0591 (Spain). 相似文献
5.
Victor Olevskii 《Integral Equations and Operator Theory》1996,25(4):496-500
We construct a continuous functionf on the circle such thatf is a Fourier multiplier inl
p
, 1<p<, but (x, y)=f(x–y) is not a Schur multiplier inS
p
,p2. 相似文献
6.
A vector valued transference of Fourier-Bessel multipliers onto Hankel multipliers with applications
Jorge J. Betancor Krzysztof Stempak 《Rendiconti del Circolo Matematico di Palermo》2002,51(1):199-206
In this note we prove a vector valued transference theorem relating Fourier-Bessel multipliers and Hankel multipliers. An
application of such a transference theorem allows to show that results of Córdoba [3] and Romera [4] can be deduced from a
recent result of Balodis and Córdoba [1, Theorem 3].
Partially supported by DGICYT Grant PB 97-1489 (Spain).
Partially supported by KBN grant # 2 PO3A 034 20. 相似文献
7.
We consider some Nikol'skij-type inequalities, thus inequalities between different metrics of a function, for almost periodic
trigonometric polynomials. Some basic methods of probability theory are applied to prove the existence of the distribution
function for an almost periodic function in the sense of Besicovitch. Finally, the Maximal function of Hardy and Littlewood
is considered and maximal inequalities on Besicovitch spaces are proved.
Received: 23 July 1998 / Revised version: 8 March 1999 相似文献
8.
Summary A recent note by Marshall and Olkin (1990), in which the Cauchy-Schwarz and Kantorovich inequalities are considered in matrix versions expressed in terms of the Loewner partial ordering, is extended to cover positive semidefinite matrices in addition to positive definite ones.Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth 相似文献
9.
We give characterizations of radial Fourier multipliers as acting on radial L
p
functions, 1 < p < 2d/(d + 1), in terms of Lebesgue space norms for Fourier localized pieces of the convolution kernel. This is a special case of
corresponding results for general Hankel multipliers. Besides L
p
− L
q
bounds we also characterize weak type inequalities and intermediate inequalities involving Lorentz spaces. Applications include
results on interpolation of multiplier spaces.
G. Garrigós partially supported by grant “MTM2007-60952” and Programa Ramón y Cajal, MCyT (Spain). A. Seeger partially supported by NSF grant DMS 0652890. 相似文献
10.
11.
Woocheol Choi 《Mathematische Nachrichten》2015,288(10):1098-1121
In this paper we obtain a refined bound for maximal functions of the multiplier operators on stratified groups and maximal functions of the multi‐parameter multipliers on product spaces of stratified groups. As an application we find a refined bound for maximal functions of joint spectral multipliers on Heisenberg group. 相似文献
12.
We study interlacing properties of the zeros of two types of linear combinations of Laguerre polynomials with different parameters, namely and . Proofs and numerical counterexamples are given in situations where the zeros of Rn, and Sn, respectively, interlace (or do not in general) with the zeros of , , k=n or n−1. The results we prove hold for continuous, as well as integral, shifts of the parameter α. 相似文献
13.
A strong type two-weight problem is solved for fractional maximal functions defined in homogeneous type general spaces. A similar problem is also solved for one-sided fractional maximal functions. 相似文献
14.
Antonios D. Melas 《Advances in Mathematics》2005,192(2):310-340
For each p>1 we precisely evaluate the main Bellman functions associated with the dyadic maximal operator on and the dyadic Carleson imbedding theorem. Actually, we do that in the more general setting of tree-like maximal operators. These provide refinements of the sharp Lp inequalities for those operators. For this we introduce an effective linearization for such maximal operators on an adequate set of functions. 相似文献
15.
Tuomas P. Hytönen 《Journal of Evolution Equations》2005,5(2):205-225
We extend the recently developed Lp-theory for the maximal regularity of the abstract Cauchy problem
and the related Fourier multiplier techniques to the real-variable Hardy space H1. Some results for Hp, 0 < p < 1, are also proved. 相似文献
16.
We prove endpoint bounds for derivatives of fractional maximal functions with either smooth convolution kernel or lacunary set of radii in dimensions . We also show that the spherical fractional maximal function maps into a first order Sobolev space in dimensions . 相似文献
17.
In this paper, we study two-weight norm inequalities for operators of potential type in homogeneous spaces. We improve some of the results given in [6] and [8] by significantly weakening their hypotheses and by enlarging the class of operators to which they apply. We also show that corresponding results of Carleson type for upper half-spaces can be derived as corollaries of those for homogeneous spaces. As an application, we obtain some necessary and sufficient conditions for a large class of weighted norm inequalities for maximal functions under various assumptions on the measures or spaces involved.Research of the first author was supported in part by NSERC grant A5149.Research of the second author was supported in part by NSF grant DMS93-02991. 相似文献
18.
We investigate in detail the mapping properties of the maximal operator associated with the heat-diffusion semigroup corresponding
to expansions with respect to multi-dimensional standard Laguerre functions . Our interest is focused on the situation when at least one coordinate of the type multi-index α is smaller than 0. For such parameters α the Laguerre semigroup does not satisfy the general theory of semigroups, and the behavior of the associated maximal operator
on L
p
spaces is found to depend strongly on both α and the dimension.
A. Nowak was supported in part by MNiSW Grant N201 054 32/4285. 相似文献
19.
In our recent paper, we introduced the notions of relative operator (α,β)-entropy and Tsallis relative operator (α,β)-entropy as a parameter extensions of relative operator entropy and Tsallis relative operator entropy. In this paper, we give upper and lower bounds of these new notions according to operator (α,β)-geometric mean introduced in Nikoufar et al. (2013) [14]. 相似文献
20.
In the present paper we deal with the polynomials Ln(α,M,N) (x) orthogonal with respect to the Sobolev inner product