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Zeitschrift für Analysis und ihre Anwendungen


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Volume 13, Issue 1, 1994, pp. 155–170
DOI: 10.4171/ZAA/519

Published online: 1994-03-31

Modular Convergence Theorems in Fractional Musielak-Orlicz Spaces

Carlo Bardaro[1] and Gianluca Vinti[2]

(1) Università degli Studi di Perugia, Italy
(2) Università degli Studi di Perugia, Italy

Here we study modular convergence in fractional Musielak-Orlicz spaces for se-quences of moment type operators and convolution operators. To obtain the requested convergence properties we give some estimates for the involved operators, using a growth condition on the convex function $\varphi$ generating the space $L^{\varphi, \alpha}$. Then the convergence theorems are obtained using a density theorem of Musielak type. For the convolution operators we also consider the line group setting.

Keywords: Fractional Musielak-Orlicz spaces, Riemann-Lioumlle and Weil fractional integrals, moment type operators, convolution operators, $h$-boundedness

Bardaro Carlo, Vinti Gianluca: Modular Convergence Theorems in Fractional Musielak-Orlicz Spaces. Z. Anal. Anwend. 13 (1994), 155-170. doi: 10.4171/ZAA/519