Approximation by matrix transforms in generalized grand Lebesgue spaces with variable exponent

References

• Iwaniec T, Sbordone C. On integrability of the Jacobian under minimal hypotheses. Arch Rational Mechanics Anal. 1992;119:129–143. doi: 10.1007/BF00375119
   Web of Science ®Google Scholar
• Greco L, Iwaniec T, Sbordone C. Inverting the p-harmonic operator. Manuscr Math. 1997;92:249–258. doi: 10.1007/BF02678192
   Web of Science ®Google Scholar
• Iwaniec T, Sbordone C. Riesz transform and elliptic PDE's with VMO coefficients. J Anal Math. 1998;74:183–212. doi: 10.1007/BF02819450
   Web of Science ®Google Scholar
• Sbordone C. Grand Sobolev spaces and their applications to variational problems. Le Matematiche. 1996;51(2):335–347.
   Google Scholar
• Sbordone C. Nonlinear elliptic equations with right hand side in nonstandard spaces. Rend Sem Math Fis. Modena: Supplemento al XLVI:1998;361–368.
   Google Scholar
• Cruz-Uribe DV, Fiorenza A. Variable Lebesgue spaces foundation and harmonic analysis. New York: Birkhäuser; 2013.
   Google Scholar
• Diening L, Harjulehto P, Hästö P. Lebesgue and Sobolev spaces with variable exponents. New York: Springer; 2011.
   Google Scholar
• Kokilashvili VM, Meskhi A, Rafeiro H, et al. Integral operators in non-standard function spaces, volumes I and II. Basel: Birkhäuser; 2016.
   Google Scholar
• Sharapudinov II. Some questions of approximation theory in the Lebesgue spaces with variable exponent. Seria Mathematicheskaya Monografia. Viladikavkaz: Itogi Nauki Yug Rossii; 2012.
   Google Scholar
• Akgun R. Trigonometric approximation of functions in generalized Lebesgue spaces with variable exponent. Ukr Math J. 2011;63(1):3–23. doi: 10.1007/s11253-011-0485-0
   Web of Science ®Google Scholar
• Akgun R. Polynomial approximation of functions in weighted Lebesgue and Smirnov spaces with nonstandard growth. Georgian Math J. 2011;18:203–235.
   Web of Science ®Google Scholar
• Akgun R, Kokilashvili VM. The refined direct and converse inequalities of trigonometric approximation in weighted variable exponent Lebesgue spaces. Georgian Math J. 2011;18:399–423.
   Web of Science ®Google Scholar
• Guven A, Israfilov DM. Trigonometric approximation in generalized Lebesgue spaces Lp(x). J Math Inequal. 2010;4(2):285–299. doi: 10.7153/jmi-04-25
   Google Scholar
• Israfilov DM, Kokilashvili VM, Samko S. Approximation in weighted Lebesgue and Smirnov spaces with variable exponents. Proceed A Razmadze Math Inst. 2007;143:25–35.
   Google Scholar
• Israfilov DM, Testici A. Approximation in Smirnov classes with variable exponent. Complex Var Elliptic Equ. 2015;60(9):1243–1253. doi: 10.1080/17476933.2015.1004539
   Web of Science ®Google Scholar
• Israfilov DM, Yirtici E. On some properties of convolutions in variable exponent Lebesgue spaces. Complex Anal Oper Theory. 2017;11:1817–1824. doi: 10.1007/s11785-017-0685-1
   Web of Science ®Google Scholar
• Israfilov DM, Testici A. Approximation problems in the Lebesgue spaces with variable exponent. J Math Anal Appl. 2018;459:112–123. doi: 10.1016/j.jmaa.2017.10.067
   Web of Science ®Google Scholar
• Israfilov DM, Testici A. Approximation by matrix transforms in weighted Lebesgue spaces with variable exponent. Results Math. 2018;73(8). Available from https://doi.org/10.1007/s00025-018-0762-4.
   Google Scholar
• Sharapudinov II. Approximation of functions in L2πp(x) by trigonometric polynomials. Izvestiya RAN Ser Math. 2013;77(2):197–224. English transl., Izvestiya : Mathematics, 77(2):407–434. doi: 10.4213/im7808
   Google Scholar
• Sharapudinov II. On direct and inverse theorems of approximation theory in variable Lebesgue space and Sobolev spaces. Azerb J Math. 2014;4(1):55–72.
   Google Scholar
• Volosivets SS. Approximation of functions and their conjugates in variable Lebesgue spaces. Sbornik Math. 2017;208(1):48–64. doi: 10.1070/SM8636
   Web of Science ®Google Scholar
• Jafarov SZ. Linear methods for summing Fourier series and approximation in weighted Lebesgue spaces with variable exponents. Ukr Math J. 2015;66(10):1509–1518. doi: 10.1007/s11253-015-1027-y
   Web of Science ®Google Scholar
• Jafarov SZ. Derivatives of a polynomial of best approximation and modulus of smoothness in generalized Lebesgue spaces with variable exponent. Demonstr Math. 2017;50(1):245–251. doi: 10.1515/dema-2017-0023
   Web of Science ®Google Scholar
• Jafarov SZ. Approximation of the functions in weighted Lebesgue spaces with variable exponent. Complex Var Elliptic Equ. 2018;63(10):1444–1458. doi: 10.1080/17476933.2017.1379999
   Web of Science ®Google Scholar
• Sharapudinov II. Approximation of functions by De Vallée Poussin means in the Lebesgue and Sobolev spaces with variable exponent. Sbornik Math. 2016;207(7):1010–1036. doi: 10.1070/SM8509
   Web of Science ®Google Scholar
• Kokilashvili VM, Meskhi A. Maximal and Calder ón–Zygmund operators in grand variable exponent Lebesgue spaces. Georgian Math J. 2014;21(4):447–461. doi: 10.1515/gmj-2014-0047
   Web of Science ®Google Scholar
• Danelia N, Kokilashvili VM. On the approximation of periodic functions within the frame of grand Lebesgue spaces. Bull Georgian Nat Acad Sci. 2012;6(2):11–16.
   Google Scholar
• Danelia N, Kokilashvili VM. Approximation by trigonometric polynomials in subspace of weighted grand Lebesgue space. Bull Georg Nation Acad Sci. 2013;7(1):11–15.
   Google Scholar
• Danelia N, Kokilashvili VM. Approximation by trigonometric polynomials in the framework of grand variable exponent Lebesgue space. Georgian Math J. 2016;23(1):43–53. doi: 10.1515/gmj-2015-0059
   Web of Science ®Google Scholar
• Israfilov DM, Testici A. Approximation in weighted generalized grand Lebesgue spaces. Colloq Math. 2016;143(1):113–126. Institute of Mathematics Polish Academy of Sciences.
   Web of Science ®Google Scholar
• Israfilov DM, Testici A. Approximation in weighted generalized grand Smirnov classes. Studia Sci Math Hungar. 2017;54(4):471–488.
   Web of Science ®Google Scholar
• Jafarov SZ. Approximation by trigonometric polynomials in subspace of variable exponent grand Lebesgue spaces. Global J Math. 2016;8(2):836–843.
   Google Scholar
• Guven A. Trigonometric approximation by matrix transforms in Lp(x) space. Anal Appl. 2012;10(1):47–65. doi: 10.1142/S0219530512500030
   Google Scholar
• Chandra P. Trigonometric approximation of functions in Lp-norm. J Math Anal Appl. 2002;275(1):13–26. doi: 10.1016/S0022-247X(02)00211-1
   Web of Science ®Google Scholar
• Guven A. Approximation in weighted Lp spaces. Rev Union Math Argent. 2012;53(1):11–23.
   Web of Science ®Google Scholar
• Leindler L. Trigonometric approximation in Lp-norm. J Math Anal Appl. 2005;302(1):129–136. doi: 10.1016/j.jmaa.2004.07.049
   Google Scholar
• Mittal ML, Rhoades BE, Mishra VN, et al. Using infinite matrices to approximate functions of class image using trigonometric polynomials. J Math Anal Appl. 2007;326(1):667–676. doi: 10.1016/j.jmaa.2006.03.053
   Web of Science ®Google Scholar
• Timan AF. Theory of approximation of functions of a real variable. New York: Macmillan; 1963.
   Google Scholar
• Zygmund A. Trigonometric series, Vol. I and II. Cambridge: University Press; 1959.
   Google Scholar