Faber–Laurent series in variable Smirnov classes

In this work, the maximal convergence properties of partial sums of Faber–Laurent series in the variableexponent Smirnov classes of analytic functions defined on a doubly connected domain of the complex plane are investigated.

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[1] Bilalov BT, Guseynov ZG. Basicity of a system of exponents with a piece-wise linear phase in variable spaces. Mediterr. J. Math. 2012; 9(3): 487-498.
[2] Bilalov BT, Gasymov TB, Guliyeva AA. On solvability of Riemann boundary value problem in Morrey-Hardy classes. Turkish Journal of Mathematics. 2016; 40(5), 1085-1101.
[3] Cruz-Uribe DV, Fiorenza A. Variable Lebesgue Spaces Foundations and Harmonic Analysis. Basel, Switzerland: Birkhäuser, 2013.
[4] Diening L. Maximal function on generalized Lebesgue spaces L p(x) . Math Inequal Appl 2004; 7(2): 245-253.
[5] Diening L, Harjulehto P, Hästö P, Michael Ruzicka M. Lebesgue and Sobolev Spaces with Variable Exponents. New York, NY, USA: Springer, 2011.
[6] Duren PL. Theory of Hp Spaces. Toronto, Ontario, Canada: General Publishing Company, 2000.
[7] Guven A, Israfilov DM. Trigonometric Approximation in Generalized Lebesgue Spaces Lp(x). Journal of Mathematical Inequalities. 2010; 4(2): 285-299.
[8] Israfilov DM. Approximation by p-Faber polynomials in the weighted Smirnov class Ep (G, ω) and the Bieberbach polynomials. Constructive approximation 2001; 17(3): 335-351.
[9] Israfilov DM. Approximation by p-Faber–Laurent Rational Functions in the Weighted Lebesgue Spaces. Czechoslovak Mathematical Journal 2004; 54(3): 751-765.
[10] Israfilov DM, Guven A. Approximation in weighted Smirnov classes. East Journal on Approximations 2005; 11(1): 91-102.
[11] Israfilov DM, Oktay B, Akgün R. Approximation in Smirnov-Orlicz classes. Glasnik Matematički 2005; 40(1): 87-102.
[12] Israfilov DM, Akgün R. Approximation in weighted Smirnov-Orlicz classes. Journal of Mathematics of Kyoto University 2006; 46(4): 755-770.
[13] Israfilov DM, Testici A. Approximation in Smirnov classes with variable exponent. Complex Var Elliptic Equ 2015; 60(9): 1243-1253.
[14] Israfilov DM, Testici A. Approximation by Faber–Laurent rational functions in Lebesgue spaces with variable exponent. Indagationes Mathematicae 2016; 27(4): 914-922.
[15] Jafarov SZ. On approximation in weighted Smirnov Orlicz classes. Complex Variables and Elliptic Equations 2012; 57(5): 567-577.
[16] Jafarov SZ. On approximation of functions by p-Faber Laurent Rattional functions. Complex Variables and Elliptic Equations 2015; 60(3): 416-428.
[17] Jafarov SZ. Approximation in weighted rearrangement invariant Smirnov spaces. Tbilisi Mathematical Journal 2016; 9 (1): 9-21.
[18] Kokilashvili V, Samko S. Weighted boundedness in Lebesgue spaces with variable exponents of classical operators on Carleson curves. Proc A Razmadze Math Inst. 2005; 138: 106-110.
[19] Sharapudinov II. Some problems of theory of approximation in the Lebesgue spaces with variable exponent. Vladikavkaz, Russia: Itogi Nauki Yug Rossi Seria Mathematicheskaya Monografia, 2012 (in Russian).
[20] Suetin PK. Series of Faber Polynomials. New York, NY, USA: Gordon and Breach Science Publishers, 1998.
[21] Warschawski S. Über das randverhalten der Ableitung der Abbildungsfunktion bei konformer Abbildung. Mathematische Zeitschrift 1932; 35(1): 321-456 (in German).
[22] Yurt H, Guven A. Approximation by Faber–Laurent rational functions on doubly connected domains. New Zealand Journal of Mathematics 2014; 44: 113-124.