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  • 1.
    Persson, Lars-Erik
    et al.
    Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
    Samko, S.G.
    Universidade do Algarve, Campus de Gambelas.
    Some new Stein and Hardy type inequalities2010In: Journal of Mathematical Sciences, ISSN 1072-3374, E-ISSN 1573-8795, Vol. 169, no 1, p. 113-129Article in journal (Refereed)
    Abstract [en]

    We prove a generalization of the pointwise Stein inequality, considering two truncated versions. More generally than in the Stein inequality, we assume that the kernel is dominated by a radial function almost decreasing after the division by a power function with nonnegative exponent in the case of the truncation to the ball of the radius and almost increasing after the multiplication by a power function in the case of truncation to the exterior of this ball. We give some applications to a series of inequalities of Hardy type in norms of various function spaces, in particular, in the norm of variable exponent Lebesgue spaces with weights.

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