On Basicity of the Perturbed System of Exponents in Morrey-Lebesgue Space

Ali Huseynli, Vidadi Mirzoyev, Aida Quliyeva

Abstract


In this work considers the Riemann boundary value problem
with the piecewise continuous coefficient in Morrey-Hardy classes. Under
some conditions on the coefficient, the Fredholmness of this problem is
studied and the general solution of homogeneous and non-homogeneous
problems in Morrey-Hardy classes is constructed. The obtained results are
applied to the study of basis properties of the system of exponents with a
piecewise linear phase in Morry-Lebesgue space.


Keywords


Morrey-Hardy classes, Riemann problem, bases, double system of exponent. 1

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References


MAZUCCATO, A. L. : Decomposition of Besov-Morrey spaces. In Harmonic Analysis

at Mount Holyake, AMS series in Contemporary Mathematics 320 (2003), 279{294.

CHEN, Y.: Regularity of the solution to the Dirichlet problem in Morrey space, J. Partial

Diff. Equations 15 (2002), 37{46.

LEMARIE-RIEUSSET, P. G.: Some remarks on the Navier-Stokes equations in R3, J.

Math. Phys. 39(8) (1988), 4108{4118.

GIGA, Y.|MIYAKAWA T.: Navier-Stokes

ow in R3 with measures as initial vorticity

and Morrey spaces, Comm. In Partial Differential Equations 14(5) (1989), 577{618.

Duoandikoetxea, J.: Weight for maximal functions and singular integrals. NCTH Summer

School on, Harmonic Analysis in Taiwan, 2005.

PEETRE, J.: On the theory of Lp; spaces, J. Funct. Anal. 4 (1964), 71{87.

ZORKO, C. T.: Morrey space, Proc. of the Amer. Math. Society 98(4) (1986), 586{592.

KY, N. X.: On approximation by trigonometric polynomials in Lp

u- spaces, Studia Sci.

Math. Hungar 28 (1993), 183{188.

KOKILASHVILI, V. | MESKHI, A.: Boundedness of maximal and singular operators

in Morrey spaces with variable exponent, Govern. College Univ., Lahore 72 (2008), 1{11.

ISRAFILOV, D.M.| TOZMAN, N.P.: Approxiamtion by polynomials in Morrey-

Smirnov classes, East J. Approx. 14(3) (2008), 255{269.

BILALOV, B.T.| QULIYEVA, A.A.: On basicity of exponential systems in Morrey type

spaces, Int. J. of Math. 25(6) (2014), 1{10.

SAMKO, N.: Weight Hardy and singular operators in Morrey spaces, J. of Math. Anal.

and Appl. 35(1) (2009), 183{188.

PONOMAREV, S. M.: On an eigen value problem, Doklady Akademii Nauk SSSR 249(5)

(1979), 1068{1070.

MOISEEV, E.I.: On some boundary value problems for mixed type equations, Diff Uravn.

(1) (1992), 123{132.

MOISEEV, E.I.: On solution of Frankle's problem in special domain, Diff. Uravn. 28(4)

(1992), 682{692.

MOISEEV, E.I.: On existence and uniqueness of solution a classical problem, Doklady

Rossiyskaya Akademiya Nauk 336(4) (1994), 448{450.

PALEY, R. | WIENER, N.: Fourier Transforms in the Complex Domain, Amer. Math.

Soc. Colloq. Publ. (Amer. Math. Soc., Providence, RI, ) 19 (1934).

LEVINSON, N.: Gap and Density Theorems, Amer. Math. Soc. Colloq. Publ. (Amer.

Math. Soc., Providence, RI, ) 29 (1940).

SEDLETSKII, A. M.: Biorthogonal expansions in series of exponents on intervals of real

axis, Usp. Mat. Nauk37:5(227) (1982), 51{95.

MOISEEV, E. I.: On basicity of the system of sines and cosines, DAN SSSR 275(4)

(1984), 794{798.

MOISEEV, E. I.: On basicity of a system of sines, Diff. Uravn. 23(1) (1987), 177{179.

BILALOV, B. T.: Basicity of some systems of exponents, cosines and sines, Diff. Uravn.

(1) (1990), 10{16.

BILALOV, B. T.: Basis properties of some systems of exponents, cosines and sines, Sib.

Math. Journal45(2) (2004), 264{273.

BILALOV, B. T.: Property of basicity in Lp of the system of exponenets, Sib. Math. J.

(1) (2006).

BILALOV, B. T.: A system of exponential functions with shift and the Kostyuchenko

problem, Sib. Math. J. 50(2) (2009), 279{288.

BILALOV, B. T.: On solution of the Kostyuchenko problem, Sib. Math. J. 53(3) (2012),

{526.

MOISEEV, E.I.: On basicity of systems of cosines and sines in weight space, Diff. Uravn.

(1) (1998), 40{44.

MOISEEV, E.I.: The basicity in the weight space of a system of eigen functions of a

differential operator., Diff. Uravn. 35(2) (1999), 200{205.

MOISEEV, E.I.: On differential properties of expansions on the system of sines and

cosines., Diff. Uravn. 32(1) (1996), 117{126.

SEDLETSKII, A. M.: Approximate properties of the system of exponents in Sobolev

spaces., Vestnik Moskovskogo Universiteta 6 (1999), 3{8.

HUSEYNOV, Z. G. | SHYKHAMMEDOV, A. M.: On bases of sines and cosines in

Sobolev spaces., Applied Mathematics Lettersa 25 (2012), 275{278.

RUSSELL, D. L.: On Exponential Bases for the Sobolev Spaces over an Interval., Journal

of Math. Analysis and Applications 87 (1982), 528-550.

HE, X.|VOLKMER, H.: Riesz bases of solutions of Sturm-Lioville equations., J.Fourier

Anal. Appl. 7(3) (2001), 297{307.

BILALOV, B.T.: On basicity of the system of exponents, cosines and sines in Lp., Dokl.

RAN 365(1) (1999), 7{8.

BILALOV, B.T.: On basicity of some systems of exponents, cosines and sines in Lp.,

Dokl. RAN 379(2) (2001), 7{9.

BILALOV, B.T.: Bases of Exponents, Cosines and Sines Which Are Eigenfunctions of

Dierential Operators., Dif. Uravn. 39(5) (2003), 1{5.

BITSADZE, A.V.: On a system of functions., UMN 5(4:38) (1950), 150{151.

BILALOV, B.T. | GASYMOV, T. | GULIYEVA A.A.: On the solvability of the Rie-

mann boundary value problem in Morrey-Hardy classes., 40 (2016), 1085{1101.

DANILYUK, I. I.: Non-regular boundary problems on the plane., Nauka,Moscow, 1975.


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