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  • 1.
    Oguntuase, James
    et al.
    Department of Mathematics, Federal University of Agriculture, Abeokuta.
    Persson, Lars-Erik
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Time scales Hardy-type inequalities via superquadracity2014In: Annals of Functional Analysis, ISSN 2008-8752, E-ISSN 2008-8752, Vol. 5, no 2, p. 61-73Article in journal (Refereed)
    Abstract [en]

    In this paper some new Hardy-type inequalities on time scales are derived and proved using the concept of superquadratic functions. Also, we extend Hardy-type inequalities involving superquadratic functions with general kernels to the case with arbitrary time scales. Several consequences of our results are given and their connection with recent results in the literature are pointed out and discussed

  • 2.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Tephnadze, George
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Wall, Peter
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    On an approximation of 2-dimensional Walsh–Fourier series in martingale Hardy spaces2018In: Annals of Functional Analysis, ISSN 2008-8752, E-ISSN 2008-8752, Vol. 9, no 1, p. 137-150Article in journal (Refereed)
    Abstract [en]

    In this paper, we investigate convergence and divergence of partial sums with respect to the 2-dimensional Walsh system on the martingale Hardy spaces. In particular, we find some conditions for the modulus of continuity which provide convergence of partial sums of Walsh-Fourier series. We also show that these conditions are in a sense necessary and suffcient. 

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