On the Fejér means of bounded Ciesielski systems

Ferenc Weisz

Studia Mathematica (2001)

  • Volume: 146, Issue: 3, page 227-243
  • ISSN: 0039-3223

Abstract

top
We investigate the bounded Ciesielski systems, which can be obtained from the spline systems of order (m,k) in the same way as the Walsh system arises from the Haar system. It is shown that the maximal operator of the Fejér means of the Ciesielski-Fourier series is bounded from the Hardy space H p to L p if 1/2 < p < ∞ and m ≥ 0, |k| ≤ m + 1. Moreover, it is of weak type (1,1). As a consequence, the Fejér means of the Ciesielski-Fourier series of a function f converges to f a.e. if f ∈ L₁ as n → ∞.

How to cite

top

Ferenc Weisz. "On the Fejér means of bounded Ciesielski systems." Studia Mathematica 146.3 (2001): 227-243. <http://eudml.org/doc/284929>.

@article{FerencWeisz2001,
abstract = {We investigate the bounded Ciesielski systems, which can be obtained from the spline systems of order (m,k) in the same way as the Walsh system arises from the Haar system. It is shown that the maximal operator of the Fejér means of the Ciesielski-Fourier series is bounded from the Hardy space $H_\{p\}$ to $L_\{p\}$ if 1/2 < p < ∞ and m ≥ 0, |k| ≤ m + 1. Moreover, it is of weak type (1,1). As a consequence, the Fejér means of the Ciesielski-Fourier series of a function f converges to f a.e. if f ∈ L₁ as n → ∞.},
author = {Ferenc Weisz},
journal = {Studia Mathematica},
keywords = {spline systems; Hardy spaces; atom; atomic decomposition; interpolation; Fejér means; Ciesielski-Fourier series; non-tangential maximal function; tempered distribution},
language = {eng},
number = {3},
pages = {227-243},
title = {On the Fejér means of bounded Ciesielski systems},
url = {http://eudml.org/doc/284929},
volume = {146},
year = {2001},
}

TY - JOUR
AU - Ferenc Weisz
TI - On the Fejér means of bounded Ciesielski systems
JO - Studia Mathematica
PY - 2001
VL - 146
IS - 3
SP - 227
EP - 243
AB - We investigate the bounded Ciesielski systems, which can be obtained from the spline systems of order (m,k) in the same way as the Walsh system arises from the Haar system. It is shown that the maximal operator of the Fejér means of the Ciesielski-Fourier series is bounded from the Hardy space $H_{p}$ to $L_{p}$ if 1/2 < p < ∞ and m ≥ 0, |k| ≤ m + 1. Moreover, it is of weak type (1,1). As a consequence, the Fejér means of the Ciesielski-Fourier series of a function f converges to f a.e. if f ∈ L₁ as n → ∞.
LA - eng
KW - spline systems; Hardy spaces; atom; atomic decomposition; interpolation; Fejér means; Ciesielski-Fourier series; non-tangential maximal function; tempered distribution
UR - http://eudml.org/doc/284929
ER -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.