By Alexandre Almeida, Luís Castro, Frank-Olme Speck

ISBN-10: 3034805152

ISBN-13: 9783034805155

This quantity is devoted to Professor Stefan Samko at the celebration of his 70th birthday. The contributions show the variety of his medical pursuits in harmonic research and operator conception. specific attention is paid to fractional integrals and derivatives, singular, hypersingular and strength operators in variable exponent areas, pseudodifferential operators in a number of smooth functionality and distribution areas, to boot as related purposes, to say yet a number of. so much contributions have been first of all awarded in meetings at Lisbon and Aveiro, Portugal, in June‒July 2011.

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Razmadze Math. Inst. 145 (2007), 109–116. [78] V. Kokilashvili and S. Samko, The maximal operator in weighted variable spaces on metric measure spaces. Proc. A. Razmadze Math. Inst. 144 (2007), 137–144. [79] V. Kokilashvili and S. Samko, On a generalization of Calder´ on-Zygmund’s theorem in weighted Lebesgue spaces with variable exponent. Bull. Georgian Natl. Acad. Sci. 175:1 (2007), 34–39. [80] V. Kokilashvili and S. Samko, Boundedness of maximal operators and potential operators on Carleson curves in Lebesgue spaces with variable exponent.

Kokilashvili where Ω ⊂ ???? is an open bounded set and ???? comes from the upper estimate for ????????(????, ????), Sobolev type estimates were proved. 15) and another ∫ ???? (????) − ???? (????) ????????(⋅) ???? (????) = ????????(????), ????(????) Ω ????????(????, ????(????, ????))[????(????, ????)] for which were found conditions of their boundednes from the Haj̷lasz-Sobolev space ???? 1,????(⋅) (????) into a Lebesgue ????????(⋅) (Ω), this being an extension of the results in [5] for the Euclidean case. In [121], 2010, there were studied H¨older spaces ???? ????(⋅) (????) on a quasimetric measure space (????, ????, ????), whose H¨older exponent ????(????) is variable.

There were obtained the conditions ∫ ∞ ∫ ???? ∣????(1, ????)∣ ???????? < ∞, ∣????(ℎ, ????)∣????(????) ???????? ≤ ????????(ℎ), 0 0 ∫ ???? ∣????(????, 1)∣????−1 ???????? ∈ ???? ???? (0, ????), 0 ensuring the boundedness of the operator ???? in ???? ???? (0, ????). In comparison with the theory of fractional type operators acting in ???????? (ℝ???? ), there naturally arise Fourier multipliers, or more speciﬁcally, multipliers with absolutely integrable Fourier transforms, when one wishes to cover the cases ???? = 1 and ???? = ∞, the class of such multipliers being also known as the Wiener algebra ˆ ???? ∈ ????1 (ℝ???? )}.

### Advances in harmonic analysis and operator theory : the Stefan Samko anniversary volume by Alexandre Almeida, Luís Castro, Frank-Olme Speck

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