Operators on radial functions
نویسندگان
چکیده
منابع مشابه
Spherical Maximal Operators on Radial Functions
where dσ is the rotationally invariant measure on Sd−1, normalized such that σ(Sd−1) = 1. Stein [5] showed that limt→0Atf(x) = f(x) almost everywhere, provided f ∈ L(R), p > d/(d − 1) and d ≥ 3. Later Bourgain [1] extended this result to the case d = 2. If p ≤ d/(d − 1) then pointwise convergence fails. However if {tj}j=1 is a fixed sequence converging to 0 then pointwise convergence may hold f...
متن کاملk-PLANE TRANSFORMS AND RELATED OPERATORS ON RADIAL FUNCTIONS
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. §
متن کاملComputing Eigenmodes of Elliptic Operators Using Radial Basis Functions
K e y w o r d s Radial basis functions, Eigenvalues, Numerical methods, Laplacian, corner singularities. 1. I N T R O D U C T I O N Many positive properties of radial basis function (RBF) methods have been identified in connection with boundary-value problems (BVPs) [1-4]. They are grid-free numerical schemes very suitable for problems in irregular geometries. They can exploit accurate and smoo...
متن کاملSquare Functions and Maximal Operators Associated with Radial Fourier Multipliers
where (Pt)t>0 is an approximation of the identity defined by the dilates of a ‘nice’ kernel (for example (Pt) may be the Poisson or the heat semigroup). Their significance in harmonic analysis, and many important variants and generalizations have been discussed in Stein’s monographs [38], [39], [44], in the survey [45] by Stein and Wainger, and in the historical article [43]. Here we focus on L...
متن کاملComposition operators acting on weighted Hilbert spaces of analytic functions
In this paper, we considered composition operators on weighted Hilbert spaces of analytic functions and observed that a formula for the essential norm, gives a Hilbert-Schmidt characterization and characterizes the membership in Schatten-class for these operators. Also, closed range composition operators are investigated.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1996
ISSN: 0377-0427
DOI: 10.1016/0377-0427(96)00047-7