M. Carmen Calderón-Moreno, Pablo J. Gerlach-Mena, José A. Prado-Bassas
Published 2018-07-25Version 1
In this paper we state the large linear and algebraic size of the family of unbounded continuous and integrable functions in $[0,+\infty)$ and of the family of sequences of these functions converging to zero uniformly on compacta and in $L^1$-norm. In addition, we put our attention on how fast can these functions grow, how smooth can they be and how strong can the convergence to zero be.
a.e. Convergence of Nörlund means with respect to Vilenkin systems of integrable functions
a.e. Convergence of $T$ means with respect to Vilenkin systems of integrable functions
Construction of Continuous, Integrable Functions with Extreme Behavior at Infinity
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