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• 1 Eötvös Loránd University Department of Numerical Analysis Pázmány P. Sétány 1/C 1117 Budapest Hungary
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## Abstract

We investigate the Kronecker product of bounded Ciesielski systems, which can be obtained from the spline systems of order (m, k) in the same way as the Walsh system from the Haar system. It is shown that the maximal operator of the Fejér means of the d-dimensional Ciesielski-Fourier series is bounded from the Hardy space Hp([0, 1)d1×…×[0, 1)dl to Lp ([0, 1)d) if 1/2<p<∞ and mj≥0, ‖kj‖≤mj+1. By an interpolation theorem, we get that the maximal operator is also of weak type (

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$(H_1^{\# _i } ,L_1 )$$ \end{document}
) (i=1,…,l), where the Hardy space
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$H_1^{\# _i }$$ \end{document}
is defined by a hybrid maximal function and
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$H_1^{\# _i } \supset L(\log L)^{l - 1}$$ \end{document}
. As a consequence, we obtain that the Fejér means of the Ciesielski-Fourier series of a function f converge to f a.e. if f
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$H_1^{\# _i }$$ \end{document}
and converge in a cone if fεL1.

• Impact Factor (2019): 0.527
• Scimago Journal Rank (2019): 0.384
• SJR Hirsch-Index (2019): 15
• SJR Quartile Score (2019): Q3 Analysis
• SJR Quartile Score (2019): Q3 Mathematics (miscellaneous)
• Impact Factor (2018): 0.702
• Scimago Journal Rank (2018): 0.47
• SJR Hirsch-Index (2018): 14
• SJR Quartile Score (2018): Q2 Mathematics (miscellaneous)

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Analysis Mathematica
Language English
Size B5
Year of
Foundation
1975
Volumes
per Year
1
Issues
per Year
4
Founder's
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245
Springer Nature Switzerland AG
Publisher's
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
ISSN 0133-3852 (Print)
ISSN 1588-273X (Online)

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