Advances in Harmonic Analysis and Operator Theory: The by V. Kokilashvili (auth.), Alexandre Almeida, Luís Castro, PDF

By V. Kokilashvili (auth.), Alexandre Almeida, Luís Castro, Frank-Olme Speck (eds.)

ISBN-10: 3034805152

ISBN-13: 9783034805155

ISBN-10: 3034805160

ISBN-13: 9783034805162

This quantity is devoted to Professor Stefan Samko at the celebration of his 70th birthday. The contributions show the variety of his clinical pursuits in harmonic research and operator concept. specific awareness is paid to fractional integrals and derivatives, singular, hypersingular and capability operators in variable exponent areas, pseudodifferential operators in numerous sleek functionality and distribution areas, in addition to comparable purposes, to say yet a couple of. so much contributions have been to start with provided in meetings at Lisbon and Aveiro, Portugal, in June‒July 2011.

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Additional resources for Advances in Harmonic Analysis and Operator Theory: The Stefan Samko Anniversary Volume

Example text

In the non-weighted case ???? = 1 there was also given a modification of this statement for convolution operators over ℝ???? with vanishing coefficients, which were already discussed in the beginning of Section 4 in the case of constant ????. In [113], 2009, there was proved that in variable exponent spaces ????????(⋅) (Ω), where ????(⋅) satisfies the log-condition and Ω is a bounded domain in R???? with the property that R???? ∖Ω has the cone property, the validity of the Hardy type 30 V. Kokilashvili inequality 1 ????(????)???? ∫ Ω ????(????) ???????? ∣???? − ????∣????−???? ????(⋅) ≦ ????∥????∥????(⋅) , ( ) ???? 0 < ???? < min 1, ????+ where ????(????) = dist(????, ∂Ω), is equivalent to a certain property of the domain Ω expressed in terms of ???? and ????Ω (close to the property that ????Ω is a pointwise multiplier in the space ???? ???? (????????(⋅) ) of Riesz potentials).

1. More on weighted estimates of potential operators. In [213], [214], 2005, there was proved the weighted ????????(⋅) (ℝ???? , ????????0 ,????∞ ) − ????????(⋅) (ℝ???? , ????????0 ,????∞ )-Sobolev theo1 1 ???? = ????(????) −???? rem with ????(????) ???? for the Riesz potential operator ???? where ????(0) ????(∞) ???? 0 , ????∞ = ????∞ , ????(0) ????(∞) ????????(∞) − ???? < ????∞ < ????[????(∞) − 1], ????????0 ,????∞ (????) = ∣????∣????0 (1 + ∣????∣)????∞ −????0 , ????0 = ????????(0) − ???? < ????0 < ????[????(0) − 1], Stefan G. Samko – Mathematician, Teacher and Man 23 under some additional condition relating the values of the exponents at the points 0 and ∞, which was removed in [203], 2007.

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. J. Integral Equations Appl.

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Advances in Harmonic Analysis and Operator Theory: The Stefan Samko Anniversary Volume by V. Kokilashvili (auth.), Alexandre Almeida, Luís Castro, Frank-Olme Speck (eds.)


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