Hardy–Sobolev inequalities for Sobolev functions in central Herz–Morrey spaces on the unit ball
نویسندگان
چکیده
Our aim in this paper is to establish Hardy-Sobolev inequalities for Sobolev functions and generalized Riesz potentials central Herz-Morrey spaces on the unit ball. As an application, we obtain norm Green potentials.
منابع مشابه
Holomorphic Mean Lipschitz Spaces and Hardy Sobolev Spaces on the Unit Ball
For points z = (z1, · · · , zn) and w = (w1, · · · , wn) in C we write 〈z, w〉 = z1w1 + · · ·+ znwn, |z| = √ |z1| + · · ·+ |zn|. Let B = {z ∈ C : |z| < 1} denote the open unit ball and let S = {ζ ∈ C : |ζ| = 1} denote the unit sphere in C. The normalized Lebesgue measures on B and S will be denoted by dv and dσ, respectively. Let H(B) denote the space of all holomorphic functions in B. Given 0 <...
متن کاملCharacterizations of Sobolev Inequalities on Metric Spaces
We present isocapacitary characterizations of Sobolev inequalities in very general metric measure spaces.
متن کاملZygmund-Type Spaces on the Unit Ball
Let H B denote the space of all holomorphic functions on the unit ball B ⊂ C. This paper investigates the following integral-type operator with symbol g ∈ H B , Tgf z ∫1 0 f tz Rg tz dt/t, f ∈ H B , z ∈ B, whereRg z ∑n j 1 zj∂g/∂zj z is the radial derivative of g. We characterize the boundedness and compactness of the integral-type operators Tg from general function spaces F p, q, s to Zygmund-...
متن کاملSobolev orthogonal polynomials defined via gradient on the unit ball
An explicit family of polynomials on the unit ball B of R is constructed, so that it is an orthonormal family with respect to the inner product 〈f, g〉 = ρ Z Bd ∇f(x) · ∇g(x)dx + L(fg), where ρ > 0, ∇ is the gradient, and L(fg) is either the inner product on the sphere S or f(0)g(0).
متن کاملA family of Sobolev orthogonal polynomials on the unit ball
A family of orthonormal polynomials on the unit ball B of R with respect to the inner product
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: Annales Fennici Mathematici
سال: 2021
ISSN: ['2737-0690', '2737-114X']
DOI: https://doi.org/10.5186/aasfm.2021.4662