Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-18T10:39:36.624Z Has data issue: false hasContentIssue false
  • English
  • Français

On Schauder bases in Hardy spaces

Published online by Cambridge University Press:  14 November 2011

P. Oswald
P. Oswald
Affiliation:
Technische Universität Dresden, Sektion Mathematik, 8027 Dresden, Mommsenstr. 13, DDR
Get access Rights & Permissions [Opens in a new window]

Synopsis

It is proved that in the case ½<p<l the periodic Franklin system forms a Schauder basis for the real Hardy space Hp(T) defined on the one-dimensional torus.

In this note we prove the following

Theorem. The periodic Franklin system forms a Schauder basis in the real Hardyspace Hp(T) defined on the one-dimensional torus if ½<p< l.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 93 , Issue 3-4 , 1983 , pp. 259 - 263
Copyright
Copyright © Royal Society of Edinburgh 1983

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Bočkarev, S. V.. Existence of basis in the space of analytic functions on the disc and some properties of Franklin system. Mat. Sb. 95 (1974), 3–18 (in Russian).Google Scholar
2Ciesielski, Z.. Bases and approximation by splines, Proc. Internat. Congr. Math.(Vancouver 1974) vol. 2, 47–51 (Montreal, Que.: Canadian Mathematical Congress, 1975).Google Scholar
3Ciesielski, Z.. Convergence of spline expansions. In Linear spaces and approximation, pp. 433–448. Int. Ser. Num. Math. 40 (Basel: Birkhäuser, 1978).Google Scholar
4Coifman, R. R.. A real variable characterization of Hp. Studia Math. 51 (1974), 269–274.Google Scholar
5Coifman, R. R. and Weiss, G.. Extensions of Hardy spaces and their use in analysis. Bull. Amer. Math. Soc. 83 (1977), 569–645.Google Scholar
6Domsta, J.. A theorem on B-splines. II. The periodic case. Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 24 (1976), 1077–1084.Google Scholar
7Oswald, P.. On inequalities for spline approximation and spline systems in the spaces Lp(0<p<1). Proc. Internat. Conf. Approx. Fund. Spaces, held in Gdansk, 1979 (to appear).Google Scholar
8Ropela, S.. Spline bases in Besov spaces. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 24 (1976), 319–325.Google Scholar
9Triebel, H.. On Haar bases in Besov spaces. Serdica 4 (1978), 330–343.Google Scholar
10Triebel, H.. Spline bases and spline representations in function spaces. Arch. Math. 36 (1981), 348–359.Google Scholar
11Triebel, H.. Spaces of Besov-Hardy-Sobolev type. Teubner-Texte Math. (Leipzig: Teubner, 1978).Google Scholar