k-PLANE TRANSFORMS AND RELATED OPERATORS ON RADIAL FUNCTIONS
نویسنده
چکیده
We prove sharp mixed norm inequalities for the k-plane transform when acting on radial functions and for potential-like operators supported in k-planes. We also study the Hardy-Littlewood maximal operator on k-planes for radial functions for which we obtain a basic pointwise inequality with interesting consequences. §
منابع مشابه
INVERSION OF k-PLANE TRANSFORMS AND APPLICATIONS IN COMPUTER TOMOGRAPHY∗
The mathematics behind Computerized Tomography (CT) is based on the study of the parallel beam transform P and the divergent beam transform D. Both of these map a function f in Rn into a function defined on the set of all lines in Rn, by integrating f along these lines. The parallel and divergent k-plane transforms are defined in a similar fashion by integration over k-planes (i.e., translates ...
متن کاملA Class of Strongly Singular Radon Transforms on the Heisenberg Group
We primarily consider here the L mapping properties of a class of strongly singular Radon transforms on the Heisenberg group H; these are convolution operators on H with kernels of the form M(z, t) = K(z)δ0(t) where K is a strongly singular kernel on C . Our results are obtained by utilizing the group Fourier transform and uniform asymptotic forms for Laguerre functions due to Erdélyi. We also ...
متن کاملA Class of compact operators on homogeneous spaces
Let $varpi$ be a representation of the homogeneous space $G/H$, where $G$ be a locally compact group and $H$ be a compact subgroup of $G$. For an admissible wavelet $zeta$ for $varpi$ and $psi in L^p(G/H), 1leq p <infty$, we determine a class of bounded compact operators which are related to continuous wavelet transforms on homogeneous spaces and they are called localization operators.
متن کاملDirectional Operators and Mixed Norms
We present a survey of mixed norm inequalities for several directional operators, namely, directional Hardy-Littlewood maximal functions and Hilbert transforms (both appearing in the method of rotations of Calderón and Zygmund), X-ray transforms, and directional fractional operators related to Riesz type potentials with variable kernel. In dimensions higher than two several interesting question...
متن کاملGeneralizations of the Fractional Calculus, Special Functions and Integral Transforms and Their Relationships
In this survey talk we aim to clarify the close relationships between the operators of the generalized fractional calculus (GFC), some classes of generalized hypergeo-metric functions and generalizations of the classical integral transforms. The GFC developed in [1] is based on the essential use of the Special Functions (SF). The generalized (multiple) fractional integrals and derivatives are d...
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