On a theorem of Marcinkiewicz and Zygmund for Taylor series
نویسندگان
چکیده
منابع مشابه
On a Theorem of Marcinkiewicz and Zygmund
The purpose of the present paper is to prove the following result: Let F(P), P= (xi, x2, • ■ • , x„), be a function harmonic for xn >0 and such that for every point Q of a set £ of positive measure on the hyperplane x„ = 0 there exists a region contained in x„>0 limited by a cone with vertex at Q and a hyperplane x„ = const, where the function is bounded. Then except for a set of measure Zero, ...
متن کاملOn Marcinkiewicz-Zygmund-Type Inequalities
We investigate the relationships between the Marcinkiewicz-Zygmund-type inequalities and certain shifted average operators. Applications to the mean boundedness of a quasi-interpolatory operator in the case of trigonometric polynomials, Jacobi polynomials, and Freud polynomials are presented.
متن کاملMarcinkiewicz-Zygmund measures on manifolds
Let X be a compact, connected, Riemannian manifold (without boundary), ρ be the geodesic distance on X, μ be a probability measure on X, and {φk} be an orthonormal (with respect to μ) system of continuous functions, φ0(x) = 1 for all x ∈ X, {`k} ∞ k=0 be an nondecreasing sequence of real numbers with `0 = 1, `k ↑ ∞ as k → ∞, ΠL := span {φj : `j ≤ L}, L ≥ 0. We describe conditions to ensure an e...
متن کاملOn Converse Marcinkiewicz-zygmund Inequalities
We obtain converse Marcinkiewicz-Zygmund inequalities such as k P kLp[ 1;1] C 0@ n X j=1 j jP (tj)j 1A1=p for polynomials P of degree n 1, under general conditions on the points ftjgj=1 and on the function . The weights f jgj=1 are appropriately chosen. We illustrate the results by applying them to extended Lagrange interpolation for exponential weights on [ 1; 1].
متن کاملMarcinkiewicz-Zygmund inequalities
We study a generalization of the classical Marcinkiewicz-Zygmund inequalities. We relate this problem to the sampling sequences in the Paley-Wiener space and by using this analogy we give sharp necessary and sufficient computable conditions for a family of points to satisfy the Marcinkiewicz-Zygmund inequalities.
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: Arkiv för Matematik
سال: 1989
ISSN: 0004-2080
DOI: 10.1007/bf02386363