The Kunze-stein Phenomenon Associated with Jacobi Transforms
نویسنده
چکیده
Recently A. D. Ionescu (2000) established the endpoint estimate for the Kunze-Stein phenomenon, which states that if G is a noncompact connected semisimple Lie group of real rank one with finite center, then L(G) ∗ L(G) ⊆ L2,∞(G). In this paper, we will prove the corresponding result for the Jacobi transform. Our method is analytical, in which we do not use the structure of Lie groups.
منابع مشابه
Hardy-type inequalities for integral transforms associated with Jacobi operator
We establish Hardy-type inequalities for the Riemann-Liouville and Weyl transforms associated with the Jacobi operator by using Hardy-type inequalities for a class of integral operators.
متن کاملNonholonomic Hamilton–jacobi Theory via Chaplygin Hamiltonization
We develop Hamilton–Jacobi theory for Chaplygin systems, a certain class of nonholonomic mechanical systems with symmetries, using a technique called Hamiltonization, which transforms nonholonomic systems into Hamiltonian systems. We give a geometric account of the Hamiltonization, identify necessary and sufficient conditions for Hamiltonization, and apply the conventional Hamilton–Jacobi theor...
متن کاملWeighted norm inequalities for integral transforms
Weighted (L, L) inequalities are studied for a variety of integral transforms of Fourier type. In particular, weighted norm inequalities for the Fourier, Hankel, and Jacobi transforms are derived from Calderón type rearrangement estimates. The obtained results keep their novelty even in the simplest cases of the studied transforms, the cosine and sine Fourier transforms. Sharpness of the condit...
متن کاملMultiparametric Wavelet Transforms
The main goal of the paper is to show that wavelet transforms and packets have the multiparametric representation in the form of a product of the rotation Jacobi matrices. These representations we call the third and the fourth canonical multiparametric form. Each multiparametric wavelet transform (MPWT) depends on several free Jacobi parameters. When parameters are changed multiparametric trans...
متن کاملAn endpoint estimate for the Kunze - Stein phenomenon and related maximal operators
One of the purposes of this paper is to prove that if G is a noncompact connected semisimple Lie group of real rank one with finite center, then L(G) ∗ L(G) ⊆ L(G). Let K be a maximal compact subgroup of G and X = G/K a symmetric space of real rank one. We will also prove that the noncentered maximal operator M2f(z) = sup z∈B 1 |B| ∫ B |f(z)| dz is bounded from L2,1(X) to L2,∞(X) and from Lp(X)...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005