IJPAM: Volume 115, No. 2 (2017)

Title

INTEGRAL OPERATORS OF HARMONIC ANALYSIS
IN SPACES DEFINED IN TERMS OF LOCAL
CHARACTERISTICS OF FUNCTIONS II

Authors

Sadiq K. Abdullayev$^1$, Elchin A. Mammadov$^2$
$^{1,2}$Department of Mechanics - Mathematics
Baku State University
Acad. Zahid Khalilov str. 23, AZ 1148, Baku, AZERBAIJAN

Abstract

In the paper we consider boundedness of subadditive operators from a rather wide class containing in particular singular integral operators, the Riesz and Bessel potentials maximal functions, fractional maximal functions, the Poisson integrals associated with Laplace-Bessel operator in new scales of Banach spaces, introduced in terms of integral characteristics of type $% \Omega _{p}^{\ast }$.

History

Received: May 17, 2017
Revised: July 2, 2017
Published: July 14, 2017

AMS Classification, Key Words

AMS Subject Classification: 42B10, 42B20, 42B35
Key Words and Phrases: subadditive operators, Riesz potential, generalized shift operators, Laplace-Bessel differential

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Bibliography

1
Abdullayev S.K., Babayev A.A. Some estimations for a singular integral with summable density. DAN SSSR, 188 (2), (1969) 263-265.

2
Abdullayev S.K., Babayev A.A. On a singular integral with summabledensity, Funksionalniy analiz i ego priminenie. Baku, (1978) 3-32.

3
Abdullayev S.K., On some classes of integral operators in space ofsummable function, DAN SSSR, 283 (4), (1985) 777-780.

4
Levitan B.M., Expansion in series by Bessel functions, and Fourierintegrals, Uspekhi Mat. Nauk, 6 (2), (1951) 102-143.

5
Levitan B.M., Generalized shift operators and some applications. M. Cos. Fiz. matlit. (1962) 323 p.

6
Kipriyanov I.A., Singular Elliptic Boundary Value Problems, M. Nauka, Fizmatlith,(1997), 18.

7
Kipriyanov I.A., Klyuchanchev M.I., Estimation of surface potentialgenerated by generalized shift operator. Dokl. AN SSSR, 188 (5), (1969) 97-100.

8
Kipriyanov I.A., Ivanov L.A., Obtaining fundamental solutions forhomogeneous equations with singularities in several variables, Proc. of S.L. Sobolev Workshop, Novosibirsk, 1 (1983), 55-77.

9
Aliyev I.A., Gadjiev A.D. Weight estimations of singular integralsgenerated by generalized shift operator, Mathematicheskiy sbornik, 183(9), (1992) 45-66.

10
Abdullayev S.K., Karamaliyev N.R. Weight estimations of singular, weakly singular operators, maximum and fractional maximum functions associated with generalized shift, Proc. Of the IV International Symposium Fourier series and their Applications. Rostov-na-Donu 28 may-3june, (2006) 44-52.

11
Abdullayev S.K., Akperov A.A., Kerimov M.K. Two-weight estimates for sub-linear operators associated with Laplace-Bessel differential operator.Vestnik Bryanskogo Gosudarstvennogo Univ. ser. exact and natural sciences.4 (2009), 6-14.

12
Abdullayev S.K., Gadjieva E.A., Isayev F.A. Two-weighted inequality for $(p; q)$- admissible $ Bk;n$-potential operators in weighted Lebesgue spaces. Fractional Differential Calculus, 2 (2016), 233-248.

13
Sadig K. Abdullayev, Elchin A. Mammadov, Integral operators of harmonic analysis in spaces defined in terms of local characteristics of functions. doi.org/10.12732/ijpam.v114i3.21

14
Sobolev S.L. Introduction to theory of cubic formulas. M.; Nauka, 1974.808 p.

How to Cite?

DOI: 10.12732/ijpam.v115i2.18 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 115
Issue: 2
Pages: 419 - 443


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