Page 1

Displaying 1 – 19 of 19

Showing per page

The Lebesgue constants for the Franklin orthogonal system

Z. Ciesielski, A. Kamont (2004)

Studia Mathematica

To each set of knots t i = i / 2 n for i = 0,...,2ν and t i = ( i - ν ) / n for i = 2ν + 1,..., n + ν, with 1 ≤ ν ≤ n, there corresponds the space ν , n of all piecewise linear and continuous functions on I = [0,1] with knots t i and the orthogonal projection P ν , n of L²(I) onto ν , n . The main result is l i m ( n - ν ) ν | | P ν , n | | = s u p ν , n : 1 ν n | | P ν , n | | = 2 + ( 2 - 3 ) ² . This shows that the Lebesgue constant for the Franklin orthogonal system is 2 + (2-√3)².

The weak type inequality for the Walsh system

Ushangi Goginava (2008)

Studia Mathematica

The main aim of this paper is to prove that the maximal operator σ is bounded from the Hardy space H 1 / 2 to weak- L 1 / 2 and is not bounded from H 1 / 2 to L 1 / 2 .

Topological Dichotomy and Unconditional Convergence

Lefevre, Pascal (1999)

Serdica Mathematical Journal

In this paper, we give a criterion for unconditional convergence with respect to some summability methods, dealing with the topological size of the set of choices of sign providing convergence. We obtain similar results for boundedness. In particular, quasi-sure unconditional convergence implies unconditional convergence.

Transplantation operators and Cesàro operators for the Hankel transform

Yuichi Kanjin (2006)

Studia Mathematica

The transplantation operators for the Hankel transform are considered. We prove that the transplantation operator maps an integrable function under certain conditions to an integrable function. As an application, we obtain the L¹-boundedness and H¹-boundedness of Cesàro operators for the Hankel transform.

Triebel-Lizorkin spaces for Hermite expansions

Jay Epperson (1995)

Studia Mathematica

This paper develops some Littlewood-Paley theory for Hermite expansions. The main result is that certain analogues of Triebel-Lizorkin spaces are well-defined in the context of Hermite expansions.

Two-parameter Hardy-Littlewood inequality and its variants

Chang-Pao Chen, Dah-Chin Luor (2000)

Studia Mathematica

Let s* denote the maximal function associated with the rectangular partial sums s m n ( x , y ) of a given double function series with coefficients c j k . The following generalized Hardy-Littlewood inequality is investigated: | | s * | | p , μ C p , α , β Σ j = 0 Σ k = 0 ( j ̅ ) p - α - 2 ( k ̅ ) p - β - 2 | c j k | p 1 / p , where ξ̅=max(ξ,1), 0 < p < ∞, and μ is a suitable positive Borel measure. We give sufficient conditions on c j k and μ under which the above Hardy-Littlewood inequality holds. Several variants of this inequality are also examined. As a consequence, the ||·||p,μ-convergence property of s m n ( x , y ) ...

Currently displaying 1 – 19 of 19

Page 1