共查询到20条相似文献,搜索用时 19 毫秒
1.
In this paper, we show weighted estimates in mixed norm spaces for the Riesz transform associated with the harmonic oscillator in spherical coordinates. In order to prove the result, we need a weighted inequality for a vector-valued extension of the Riesz transform related to the Laguerre expansions that is of independent interest. The main tools to obtain such an extension are a weighted inequality for the Riesz transform independent of the order of the involved Laguerre functions and an appropriate adaptation of Rubio de Francia’s extrapolation theorem. 相似文献
2.
Ó scar Ciaurri Krzysztof Stempak 《Transactions of the American Mathematical Society》2006,358(10):4441-4465
Proved are weighted transplantation inequalities for Fourier-Bessel expansions. These extend known results on this subject by considering the largest possible range of parameters, allowing more weights and admitting a shift. The results are then used to produce a fairly general multiplier theorem with power weights for considered expansions. Also fractional integral results and conjugate function norm inequalities for these expansions are proved.
3.
Regularity properties of Laguerre means are studied in terms of certain Sobolev spaces defined using Laguerre functions. As
an application we prove a localization theorem for Laguerre expansions. 相似文献
4.
本文通过建立与特殊Hermite展开相对应的Littlewood-Paley分解和相关的扭曲卷积核的L2估计,得到特殊Hermite展开的乘子定理,作为该结果的应用,给出了Hermite函数及Laguerre函数展开的乘子定理。 相似文献
5.
Krzysztof Stempak 《Journal of Fourier Analysis and Applications》2011,17(3):408-430
In this survey article we overview transplantation theorems for several types of continuous and discrete orthogonal expansions.
These include: Hankel and Dunkl transforms, and Fourier-Bessel, Jacobi and Laguerre expansions. We also discuss the idea of
transference of transplantation and point out how a notion of conjugacy for orthogonal expansions may be interpreted as a
generalized transplantation. 相似文献
6.
The weak type (1,1) estimate for special Hermite expansions on Cn is proved by using the Calderón-Zygmund decomposition. Then the multiplier theorem in Lp(1
相似文献
7.
《Journal de Mathématiques Pures et Appliquées》2005,84(3):375-405
We study different Sobolev spaces associated with multidimensional Laguerre expansions. To do this we establish an analogue of P.A. Meyer's multiplier theorem, prove some transference results between higher order Riesz–Hermite and Riesz–Laguerre transforms, and introduce fractional derivatives and integrals corresponding to the Laguerre setting. Hypercontractivity of the Laguerre semigroups and Calderón's reproduction formula are also discussed. 相似文献
8.
S Thangavelu 《Proceedings Mathematical Sciences》1993,103(3):303-320
Regularity properties of twisted spherical means are studied in terms of certain Sobolev spaces defined using Laguerre functions. As an application we prove a localisation theorem for special Hermite expansions. 相似文献
9.
The weak type (1,1) estimate for special Hermite expansions on Cn is proved by using the Calder/'on-Zygmund decomposition. Then the multiplier theorem in Lp(lpα) is obtained. The special Mermite expansions in twisted Hardy space are also considered. As an application, the multipliers for a certain kind of Laguerre expansions are given in Lp space. 相似文献
10.
The weak type (1,1) estimate for special Hermite expansions on Cn is proved by using the Calder/'on-Zygmund decomposition. Then the multiplier theorem in Lp(lpα) is obtained. The special Mermite expansions in twisted Hardy space are also considered. As an application, the multipliers
for a certain kind of Laguerre expansions are given in Lp space. 相似文献
11.
BłAŻEJ JAN WRÓBEL 《Proceedings Mathematical Sciences》2011,121(1):45-75
We examine weighted L
p
boundedness of g-functions based on semigroups related to multi-dimensional Laguerre function expansions of Hermite type. A technique of vector-valued
Calderón–Zygmund operators is used. 相似文献
12.
本文通过建立与广义Sublaplace算子L相关的Litlewood-Paley理论,得到L的谱乘子定理,作为该结果的应用,并给出一类Laguere函数展开的乘子定理 相似文献
13.
Antoine Gournay 《Potential Analysis》2016,44(1):109-136
We study potential operators associated with Laguerre function expansions of convolution and Hermite types, and with Dunkl-Laguerre expansions. We prove qualitatively sharp estimates of the corresponding potential kernels. Then we characterize those 1 ≤ p,q ≤ 8, for which the potential operators are L p - L q bounded. These results are sharp analogues of the classical Hardy-Littlewood-Sobolev fractional integration theorem in the Laguerre and Dunkl-Laguerre settings. 相似文献
14.
M.E Cohen 《Journal of Mathematical Analysis and Applications》1984,102(1):123-133
The paper deals with general expansions which give as special cases new results involving the Bessel functions, Jacobi, ultraspherical, and Laguerre polynomials, where the degree of the function is incorporated in the argument. In fact, the theorems unify and extend the Neumann-Gegenbauer expansion and its generalization by Fields and Wimp, Cohen, and others, the Kapteyn expansion theory, and the Kapteyn expansion of the second kind. New expressions are given for the Neumann-type degenerate form of a Gegenbauer addition theorem, the Feldheim expansions for the Jacobi and ultraspherical polynomials, and other expressions. Also of interest is the new method of proof, involving differential and integral operators. 相似文献
15.
Krzysztof Stempak 《Monatshefte für Mathematik》1996,122(2):187-197
We supplement our previous paper [9] by adding a theorem that transplantsL
p
-norm maximal inequalities for Laguerre multipliers. As an immediate consequence we obtain negative results concerningL
p
-estimates of partial sum maximal operators for Laguerre expansions.Research supported in part by KBN grant No. 2 PO3A 030 09. 相似文献
16.
V. Pati A. Sitaram M. Sundari S. Thangavelu 《Journal of Fourier Analysis and Applications》1995,2(5):427-433
In this paper, we extend a theorem of Hardy’s on Fourier transform pairs to: (a) a noncompact-type Riemannian symmetric space
of rank one, with respect to the eigenfunction expansion of the invariant Laplacian; (b) a compact Riemannian manifold with
respect to the eigenfunction expansion of a positive elliptic operator; and (c) Rn with respect to Hermite and Laguerre expansions. 相似文献
17.
For a family of weight functions invariant under a finite reflection group, the boundedness of a maximal function on the unit sphere is established and used to prove a multiplier theorem for the orthogonal expansions with respect to the weight function on the unit sphere. Similar results are also established for the weighted space on the unit ball and on the standard simplex. 相似文献
18.
Joseph R. Litko 《Queueing Systems》1989,4(4):367-381
Queue length and interdeparture distributions for GI/G/1 are obtained using the Laguerre function expansion of the waiting time distribution. The expansion of the steady state waiting time distribution is obtained here by solving a small set of linear equations in the Laguerre function expansion coefficients. Examples show the accuracy of the results and illustrate purely numerical techniques for obtaining the necessary expansions of the arrival and service distributions. 相似文献
19.
20.
Jorge J. Betancor Juan C. Fariña Lourdes Rodríguez-Mesa Alejandro Sanabria-García 《Journal of Fourier Analysis and Applications》2008,14(4):493-513
In this paper we establish transference results showing that the boundedness of the conjugate operator associated with Hankel
transforms on Lorentz spaces can be deduced from the corresponding boundedness of the conjugate operators defined on Laguerre,
Jacobi, and Fourier–Bessel settings. Our result also allows us to characterize the power weights in order that conjugation
associated with Laguerre, Jacobi, and Fourier–Bessel expansions define bounded operators between the corresponding weighted
L
p
spaces.
This paper is partially supported by MTM2004/05878. Third and fourth authors are also partially supported by grant PI042004/067. 相似文献