Abstract
A system of exponents with a piecewise linear phase is considered in the paper. The criteria of basicity, completeness and minimality of this system in Lebesgue space of functions with variable summability exponent are established.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bilalov B.T.: Basicity of some systems of exponents, cosines and sines. Differ. Uravn. 26(1), 10–16 (1990)
Bilalov B.T.: Basis properties of some system of exponents cosines and sines. Sibirsk. Mat. Zh. 45(2), 264–273 (2004)
Bilalov B.T., Guseynov Z.G.: Bases from exponent in Lebesque spaces of functions with variable summability exponents. Trans. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci. XXVIII(1), 43–48 (2008)
Bilalov B.T., Salmanov V.F.: Uniform convergence of biorthogonal series on one system of exponents. Trans. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci. XXIII(4), 25–34 (2003)
Danilyuk I.I.: Nonregular boundary value problems on plane. Nauka, Moscow (1975)
Devdariani G.G.: On basicity of a system of functions. Differ. Uravn. 22(1), 170–171 (1987)
Diening L., Ruzicka M.: Calderon – Zigmund operators on generalized Lebesgue spaces L p(·) and problems related to fluid dynamics. J. Reine Angew. Math. 563, 197–220 (2003)
Gakhov F.D.: Boundary value problems. Nauka, Moscow (1977)
Kokilashvili V., Samko S.: Singular Integrals in Weighted Lebesgue Spaces with Variable Exponent. Georgian Math. J. 10(1), 145–156 (2003)
Kovacik O., Rakosnik J.: On Spaces L p(x) and W m,p(x). Czechoslovak Math. J. 116(41), 592–618 (1991)
Levin B.Ya.: Distribution of the roots of entire functions. GITTL, Moscow (1956)
Moiseev E.I.: Basicity of the system of exponents, cosines and sines in L p . Dokl. Akad. Nauk 275(4), 794–798 (1984)
Sedletskii A.M.: Biorthogonal expansion in series of exponents on the intervals of a real axis. Uspekhi Mat. Nauk 37(227), 51–95 (1982)
Sharapudinov I.I.: On uniform boundedness in L p (p = p (x)) of some families of convolution operators. Mat. Zametki 59(2), 291–302 (1996)
Sharapudinov I.I.: On topology of the space \({\mathcal{L}^{p(x)} ([0, 1])}\) . Mat. Zametki 26(4), 613–632 (1979)
Sharapudinov I.I.: On some problems of approximation theory in the spaces L p(x) (E). Anal. Math. 33(2), 135–153 (2007)
Wiener N., Paley R: Fourier transform in complex plane. Nauka, Moscow (1964)
Xianling F., Dun Z.: On the spaces L p(x) (Ω) and W m,p(x) (Ω). J. Math. Anal. Appl. 263, 424–446 (2001)
Zhikov V.V.: Averaging of variational calculus and theory of elasticity functionals. Izv. Ross. Akad. Nauk Ser. Mat. 50(4), 675–710 (1986)
Zhikov V.V.: Meier type estimations for solving Stockes nonlinear system. Differ. Uravn. 33(1), 107–114 (1997)
Zhikov V.V.: On some variational problems. Russ. J. Math. Phys. 5(1), 105–116 (1997)
Zhikov V.V., Pastukhova S.E.: On increased summability of the gradient of solution of elliptic equations with variable nonlinearity exponent. Mat. Sb. 199(12), 19–52 (2008)
Zhikov V.V., Pastukhova S.E.: On Trotter-Kato theorem in variable space. Funct. Anal. Appl 41(4), 22–29 (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bilalov, B.T., Guseynov, Z.G. Basicity of a System of Exponents with a Piecewise Linear Phase in Variable Spaces. Mediterr. J. Math. 9, 487–498 (2012). https://doi.org/10.1007/s00009-011-0135-7
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00009-011-0135-7