On the Range of the Chébli–Trimèche Transform

We first characterise the L²-Schwartz functions whose image under the Chébli–Trimèche transform are compactly supported smooth functions. We then generalise a theorem by H. H. Bang, characterising the smooth L^p-functions whose (distributional) transform have compact support.     

On the Range of the Chébli–Trimèche Transform

We first characterise the L²-Schwartz functions whose image under the Chébli–Trimèche transform are compactly supported smooth functions. We then generalise a theorem by H. H. Bang, characterising the smooth L^p-functions whose (distributional) transform have compact support.The author is supported by a research grant from the Australian Research Council.     

On real Paley-Wiener theorems for certain integral transforms

We prove real Paley-Wiener theorems for the (inverse) Jacobi transform, characterising the space of L²-functions whose image under the Jacobi transform are (smooth) functions with compact support.     

Weyl transforms associated with the Hankel transform in Clifford analysis

In this paper, we define the Hankel–Wigner transform in Clifford analysis and therefore define the corresponding Weyl transform. We present some properties of this kind of Hankel–Wigner transform, and then give the criteria of the boundedness of the Weyl transform and compactness on the L^p space. Copyright © 2005 John Wiley & Sons, Ltd.     

Hardy-type spaces for eigenfunctions of invariant differential operators on homogeneous line bundles over Hermitian symmetric spaces

We prove a Fatou-type theorem on a homogeneous line bundle over a Hermitian symmetric space, and characterize the range of the Poisson transform of L_p -functions on the maximal boundary as a Hardy-type space.     

Real Paley-Wiener theorems associated with the weinstein operator

In this paper we use real analysis techniques to establish a new real Paley-Wiener theorems for the Fourier-Bessel transform associated with the Weinstein operator. More precisely we characterize the C ^∞-functions whose image under the Fourier-Bessel transform are functions with compact support through an L ^p growth condition, p ∈ [1, +∞] and we give another version of the real Paley-Wiener theorem for L ²-functions.     

Lusin type and cotype for Laguerre <Emphasis Type="Italic">g</Emphasis>-functions

We characterize Lusin type and cotype for a Banach space in terms of the L ^p -boundedness of Littlewood-Paley g-functions associated with the Hermite and Laguerre expansions.     

Potential operators associated with Hankel and Hankel-Dunkl transforms

We study Riesz and Bessel potentials in the settings of Hankel transform, modified Hankel transform and Hankel-Dunkl transform. We prove sharp or qualitatively sharp pointwise estimates of the corresponding potential kernels. Then we characterize those 1 ≤ p, q≤∞, for which the potential operators satisfy L ^p -L ^q estimates. In case of the Riesz potentials, we also characterize those 1 ≤ p, q ≤ ∞, for which two-weight L ^p -L ^q estimates, with power weights involved, hold. As a special case of our results, we obtain a full characterization of two power-weight L ^p -L ^q bounds for the classical Riesz potentials in the radial case. This complements an old result of Rubin and its recent reinvestigations by De Nápoli, Drelichman and Durán, and Duoandikoetxea.     

Espaces de Banach stables

We define the notion of “stable Banach space” by a simple condition on the norm. We prove that ifE is a stable Banach space, then every subspace ofL ^p(E) (1≦p<∞) is stable. Our main result asserts that every infinite dimensional stable Banach space containsl ^p, for somep, 1≦p<∞. This is a generalization of a theorem due to D. Aldous: every infinite dimensional subspace ofL ¹ containsl ^p, for somep in the interval [1, 2].     

Spectral Multipliers for Multidimensional Bessel Operators

In this paper we prove L ^p -boundedness properties of spectral multipliers associated with multidimensional Bessel operators. In order to do this we estimate the L ^p -norm of the imaginary powers of Bessel operators. We also prove that the Hankel multipliers of Laplace transform type on (0,∞) ⁿ are principal value integral operators of weak type (1,1).     

ON CONVERGENCE OF WAVELET PACKET EXPANSIONS

It is well known that the-Walsh-Fourier expansion of a function from the block spaceB _q([0,1]), 1B _q in certain periodized smooth periodic non-stationary wavelet packets bases based on the Haar filters. We also consider wavelet packets based on the Shannon filters and show that the expansion of L^p-functions, 1相似文献   

Critical p-adic L-functions

We attach p-adic L-functions to critical modular forms and study them. We prove that those L-functions fit in a two-variables p-adic L-function defined locally everywhere on the eigencurve.     

Spectral analysis of the finite Hankel transform and circular prolate spheroidal wave functions

In this paper, we develop two practical methods for the computation of the eigenvalues as well as the eigenfunctions of the finite Hankel transform operator. These different eigenfunctions are called circular prolate spheroidal wave functions (CPSWFs). This work is motivated by the potential applications of the CPSWFs as well as the development of practical methods for computing their values. Also, in this work, we should prove that the CPSWFs form an orthonormal basis of the space of Hankel band-limited functions, an orthogonal basis of L²([0,1]) and an orthonormal system of L²([0,+∞[). Our computation of the CPSWFs and their associated eigenvalues is done by the use of two different methods. The first method is based on a suitable matrix representation of the finite Hankel transform operator. The second method is based on the use of an efficient quadrature method based on a special family of orthogonal polynomials. Also, we give two Maple programs that implement the previous two methods. Finally, we present some numerical results that illustrate the results of this work.     

Hankel Operators on Fock Spaces and Related Bergman Kernel Estimates

Hankel operators with anti-holomorphic symbols are studied for a large class of weighted Fock spaces on ? ⁿ . The weights defining these Hilbert spaces are radial and subject to a mild smoothness condition. In addition, it is assumed that the weights decay at least as fast as the classical Gaussian weight. The main result of the paper says that a Hankel operator on such a Fock space is bounded if and only if the symbol belongs to a certain BMOA space, defined via the Berezin transform. The latter space coincides with a corresponding Bloch space which is defined by means of the Bergman metric. This characterization of boundedness relies on certain precise estimates for the Bergman kernel and the Bergman metric. Characterizations of compact Hankel operators and Schatten class Hankel operators are also given. In the latter case, results on Carleson measures and Toeplitz operators along with Hörmander’s L ² estimates for the $\bar{\partial}$ operator are key ingredients in the proof.     

Hilbert transform and related topics associated with the differential Jacobi operator on (0, +∞)

We define Hilbert transform and conjugate Poisson integrals associated with the Jacobi differential operator on (0, +∞). We prove that these operators are bounded in the appropriate Lebesgue spaces L ^p , 1 < p < +∞. In this study, the tools used are the Littlewood–Paley g-functions associated with the Poisson semigroup and the supplementary Poisson semigroup which we introduce in this paper.     

The Definition of the Fourier Transform for Weighted Inequalities

Weighted norm inequalities for the Fourier transform have a long history, motivated in part by generalizations of the differentiation formula for Fourier transforms and by applications such as Kolmogorov′s prediction theory and restriction theory. Typically, a norm inequality, || ||L^q_μ ≤ ||f||L^p_v, is established on a subspace of L¹ contained in the weighted space L^p_v, where is the Fourier transform and μ and v are weights. The problem of defining the extension of on all of L^p_v is posed and solved here for several important cases. This definition sometimes results in the ordinary distributional Fourier transform, but there are other situations which are also analyzed. Precise necessary conditions and closure theorems are inextricably related to this program, and these results are established.     

Multi-window dilation-and-modulation frames on the half real line

Wavelet and Gabor systems are based on translation-and-dilation and translation-and-modulation operators, respectively, and have been studied extensively. However, dilation-and-modulation systems cannot be derived from wavelet or Gabor systems. This study aims to investigate a class of dilation-and-modulation systems in the causal signal space L²(ℝ₊). L²(ℝ₊) can be identified as a subspace of L²(ℝ), which consists of all L²(ℝ)-functions supported on ℝ₊ but not closed under the Fourier transform. Therefore, the Fourier transform method does not work in L²(ℝ₊). Herein, we introduce the notion of Θ_a-transform in L²(ℝ₊) and characterize the dilation-and-modulation frames and dual frames in L²(ℝ₊) using the Θ_a-transform; and present an explicit expression of all duals with the same structure for a general dilation-and-modulation frame for L²(ℝ₊). Furthermore, it has been proven that an arbitrary frame of this form is always nonredundant whenever the number of the generators is 1 and is always redundant whenever the number is greater than 1. Finally, some examples are provided to illustrate the generality of our results.

     

Plancherel Formula for Berezin Deformation of L on Riemannian Symmetric Space

Consider natural representations of the pseudounitary group U(p, q) in the space of holomorphic functions on the Cartan domain (Hermitian symmetric space) U(p, q)/(U(p)×U(q)). Berezin representations of O(p, q) are the restrictions of such representations to the subgroup O(p, q). We obtain the explicit Plancherel formula for the Berezin representations. The support of the Plancherel measure is a union of many series of representations. The density of the Plancherel measure on each piece of the support is an explicit product of Γ-functions. We also show that the Berezin representations give an interpolation between L² on noncompact symmetric space O(p, q)/O(p)×O(q) and L² on compact symmetric space O(p+q)/O(p)×O(q).     

The essential norm of Hankel operator on the Bergman spaces of strongly pseudoconvex domains

Let D be a bounded strongly pseudoconvex domain with smooth boundary in Cⁿ and let fL²(D). For the Hankel operator H_f on the Bergman space A²(D), it is shown that the essential norm of H_f in L²(D) is comparable to the distance norm from H_f to compact Hankel operators. The result extends the previous corresponding version in the disc proved by Lin and Rochberg in Integ.Equat.Oper.Theory 361–372,17 (1993).     

Uniform estimates on multi-linear operators with modulation symmetry

In a previous paper [20] in this series, we gaveL ^p estimates for multi-linear operators given by multipliers which are singular on a non-degenerate subspace of some dimensionk. In this paper, we give uniform estimates when the subspace approaches a degenerate region in the casek = 1, and when all the exponentsp are between 2 and ∞. In particular, we recover the non-endpoint uniform estimates for the bilinear Hubert transform in [12]. Dedicated to Tom Wolff