On the Multiplier Space Generated by the Rademacher System

2004 ◽  
Vol 75 (1/2) ◽  
pp. 158-165 ◽  
Author(s):  
S. V. Astashkin
Keyword(s):  
Rademacher System ◽  
Multiplier Space

scholarly journals The αAB-, βAB-, γab- and NAB-duals for sequence spaces

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6219-6231
Author(s):  
D. Foroutannia ◽  
H. Roopaei
Keyword(s):  
Sequence Spaces ◽  
The Other ◽  
Infinite Matrices ◽  
Multiplier Space

Let A = (an,k) and B = (bn,k) be two infinite matrices with real entries. The main purpose of this paper is to generalize the multiplier space for introducing the concepts of ?AB-, ?AB-, ?AB-duals and NAB-duals. Moreover, these duals are investigated for the sequence spaces X and X(A), where X ? {c0, c, lp} for 1 ? p ? ?. The other purpose of the present study is to introduce the sequence spaces X(A,?) = {x=(xk): (?x?k=1 an,kXk - ?x?k=1 an-1,kXk)? n=1 ? X}, where X ? {l1,c,c0}, and computing the NAB-(or Null) duals and ?AB-duals for these spaces.

scholarly journals The n-th derivative characterisation of Möbius invariant Dirichlet space

1998 ◽  
Vol 58 (1) ◽  
pp. 43-56 ◽  
Author(s):  
Rauno Aulaskari ◽  
Maria Nowak ◽  
Ruhan Zhao
Keyword(s):  
Carleson Measure ◽  
Bloch Space ◽  
Dirichlet Space ◽  
Function Spaces ◽  
Multiplier Space ◽  
Little Bloch Space ◽  
Special Parameter

In this paper we give the n-th derivative criterion for functions belonging to recently defined function spaces Qp and Qp, 0. For a special parameter value p = 1 this criterion is applied to BMOA and VMOA, and for p > 1 it is applied to the Bloch space and the little Bloch space . Further, a Carleson measure characterisation is given to Qp, and in the last section the multiplier space from Hq into Qp is considered.

Extraction of subsystems “Majorized” by the rademacher system

1999 ◽  
Vol 65 (4) ◽  
pp. 407-417 ◽  
Author(s):  
S. V. Astashkin
Keyword(s):  
Rademacher System

scholarly journals About interpolation of subspaces of rearrangement invariant spaces generated by Rademacher system

2001 ◽  
Vol 25 (7) ◽  
pp. 451-465 ◽  
Author(s):  
Sergey V. Astashkin
Keyword(s):  
Invariant Function ◽  
Function Spaces ◽  
Interpolation Theory ◽  
Rearrangement Invariant Spaces ◽  
Rademacher System ◽  
Rearrangement Invariant Function Spaces ◽  
One To One ◽  
Rademacher Series ◽  
Invariant Spaces

The Rademacher series in rearrangement invariant function spaces “close” to the spaceL∞are considered. In terms of interpolation theory of operators, a correspondence between such spaces and spaces of coefficients generated by them is stated. It is proved that this correspondence is one-to-one. Some examples and applications are presented.

scholarly journals Applications of Affine Systems of Walsh Type to Generate Smooth Basis

2021 ◽  
pp. 4875-4884
Author(s):  
Khaled Hadi ◽  
Saad Nagy
Keyword(s):  
Generating Function ◽  
Riesz Basis ◽  
Walsh System ◽  
Continuous Periodic Function ◽  
Affine Systems ◽  
Rademacher System ◽  
Almost Everywhere ◽  
Affine System ◽  
Smooth Basis ◽  
Differential Properties

The question on affine Riesz basis of Walsh affine systems is considered. An affine Riesz basis is constructed, generated by a continuous periodic function that belongs to the space on the real line, which has a derivative almost everywhere; in connection with the construction of this example, we note that the functions of the classical Walsh system suffer a discontinuity and their derivatives almost vanish everywhere. A method of regularization (improvement of differential properties) of the generating function of Walsh affine system is proposed, and a criterion for an affine Riesz basis for a regularized generating function that can be represented as a sum of a series in the Rademacher system is obtained.

Predual of the Multiplier Algebra of Ap(G) and Amenability

2004 ◽  
Vol 56 (2) ◽  
pp. 344-355 ◽  
Author(s):  
Tianxuan Miao
Keyword(s):  
Banach Space ◽  
Compact Group ◽  
Linear Span ◽  
Locally Compact Group ◽  
Locally Compact ◽  
Multiplier Algebra ◽  
Norm Closure ◽  
Multiplier Space ◽  
Dual Banach Space

AbstractFor a locally compact group G and 1 < p < ∞, let Ap(G) be the Herz-Figà-Talamanca algebra and let PMp(G) be its dual Banach space. For a Banach Ap(G)-module X of PMp(G), we prove that the multiplier space ℳ(Ap(G); X*) is the dual Banach space of QX, where QX is the norm closure of the linear span Ap(G)X of u f for u 2 Ap(G) and f ∈ X in the dual of ℳ(Ap(G); X*). If p = 2 and PFp(G) ⊆ X, then Ap(G)X is closed in X if and only if G is amenable. In particular, we prove that the multiplier algebra MAp(G) of Ap(G) is the dual of Q, where Q is the completion of L1(G) in the ‖ · ‖M-norm. Q is characterized by the following: f ∈ Q if an only if there are ui ∈ Ap(G) and fi ∈ PFp(G) (i = 1; 2, … ) with such that on MAp(G). It is also proved that if Ap(G) is dense in MAp(G) in the associated w*-topology, then the multiplier norm and ‖ · ‖Ap(G)-norm are equivalent on Ap(G) if and only if G is amenable.

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