Homogeneous Besov Spaces associated with the spherical mean operator
نویسندگان
چکیده
منابع مشابه
Spaces of DLp type and a convolution product associated with the spherical mean operator
where Sn is the unit sphere {(η,ξ) ∈R×Rn : η2 +‖ξ‖2 = 1} in Rn+1 and σn is the surface measure on Sn normalized to have total measure one. This operator plays an important role and has many applications, for example, in image processing of so-called synthetic aperture radar (SAR) data (see [7, 8]), or in the linearized inverse scattering problem in acoustics [6]. In [10], the authors associate ...
متن کاملThe spherical mean value operator with centers on a sphere
Let B represent the ball of radius ρ in Rn and S its boundary; consider the map M : C∞ 0 (B) → C∞(S × [0,∞)) where (Mf)(p, r) = 1 ωn−1 ∫ |θ|=1 f(p+ rθ) dθ represents the mean value of f on a sphere of radius r centered at p. We summarize and discuss the results concerning the injectivity of M, the characterization of the range of M, and the inversion of M. There is a close connection between me...
متن کاملImage Decompositions Using Bounded Variation and Generalized Homogeneous Besov Spaces
This paper is devoted to the decomposition of an image f into u+ v, with u a piecewise-smooth or “cartoon” component, and v an oscillatory component (texture or noise), in a variational approach. Y. Meyer [Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear Evolution Equations, University Lecture Series, vol. 22, Amer. Math. Soc., Providence, RI, 2001] proposed refinements of the t...
متن کاملUniqueness Property for Spherical Homogeneous Spaces
Let G be a connected reductive group. Recall that a homogeneous G-space X is called spherical if a Borel subgroup B ⊂ G has an open orbit on X . To X one assigns certain combinatorial invariants: the weight lattice, the valuation cone and the set of B-stable prime divisors. We prove that two spherical homogeneous spaces with the same combinatorial invariants are equivariantly isomorphic. Furthe...
متن کاملOperator-valued Fourier Multipliers in Besov Spaces and Its Applications
In recent years, Fourier multiplier theorems in vector–valued function spaces have found many applications in embedding theorems of abstract function spaces and in theory of differential operator equations, especially in maximal regularity of parabolic and elliptic differential–operator equations. Operator–valued multiplier theorems in Banach–valued function spaces have been discussed extensive...
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: Cubo (Temuco)
سال: 2011
ISSN: 0719-0646
DOI: 10.4067/s0719-06462011000200001