Advances in harmonic analysis and operator theory : the by Alexandre Almeida, Luís Castro, Frank-Olme Speck

By Alexandre Almeida, Luís Castro, Frank-Olme Speck

This quantity is devoted to Professor Stefan Samko at the get together of his 70th birthday. The contributions demonstrate the variety of his medical pursuits in harmonic research and operator conception. specific attention is paid to fractional integrals and derivatives, singular, hypersingular and power operators in variable exponent areas, pseudodifferential operators in a number of sleek functionality and distribution areas, to boot as related purposes, to say yet a couple of. such a lot contributions have been to start with offered in meetings at Lisbon and Aveiro, Portugal, in June‒July 2011.

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One of the ways was to introduce such space ????????),???? (Ω, ⟨????⟩−???? ) with ⟨????⟩ = 1 + ∣????∣2 via the norm sup 0 0 for ???? > 0 and ????(0) = 0. 34 V. Kokilashvili There was also given a version of weighted grand Lebesgue spaces, different from the usual ones, for bounded sets, in which together with the passage from ???? to ???? − ???? a weight also depending on ???? was introduced. In both the versions, by means of the Stein-Weiss interpolation theorem with change of measure, it was shown that linear operators bounded in a Lebesgue space with Muckenhoupt weights are also bounded in the corresponding grand Lebesgue space with a Muckenhoupt weight.

Razmadze Math. Inst. 151 (2009), 134–138. [87] V. Kokilashvili and S. Samko, Boundedness of weighted singular integral operators on a Carleson curves in Grand Lebesgue spaces. In ICNAAM 2010: Intern. Conf. Numer. Anal. Appl. , vol. 1281, pp. 490–493. AIP Confer. , 2010. [88] V. Kokilashvili and S. Samko, Boundedness of weighted singular integral operators in Grand Lebesgue spaces. Georgian Math. J. 18:2 (2011), 259–269. S. G. Samko, A condition for the absolute integrability of Fourier integrals.

24] D. Israfilov, V. Kokilashvili, and S. Samko, Approximation in weighted Lebesgue and Smirnov spaces with variable exponents. Proc. A. Razmadze Math. Inst. 143 (2007), 25–35. A. G. I. Kheifits, Nikolai Vasilievich Govorov. In memory of a scholar, friend and teacher. Izv. Severo-Kavkaz. Nauchn. Tsentra Vyssh. Shkoly Estestv. Nauk. 1988:4 (1988), 65–70, 143. K. A. Kilbas, M. G. Samko, Upper and lower bounds for solutions of nonlinear Volterra convolution integral equations with power nonlinearity.

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