WEIGHTED INEQUALITIES FOR THE TRACES OF FUNCTIONS REPRESENTED BY THE RIESZ GENERALIZED POTENTIALS


Abstract views: 43 / PDF downloads: 34

Authors

  • Bahruz Agarzayev Azerbaijan State Maritime Academy, Baku, Azerbaijan
  • Gulnar Mirzayeva Academy of Public Administration under the President of the Republic of Azerbaijan
  • Aynur Abdullayeva Azerbaijan State Maritime Academy, Baku, Azerbaijan
  • Gojayeva Khadija Azerbaijan State Pedagogical University, Baku, Azerbaijan
  • Bagirova Sabira The Academy of Republic Administration under the President of the Republic of Azerbaijan

Keywords:

Generalized Riesz potential, weight spaces, locally summable function, function trace, harmonic analysis.

Abstract

The theory of potentials has wide applications in singular integral operators and harmonic analysis. In this context, the Riesz potential inclusion theorems play an important role. Generalized Riesz potentials associated with the Laplace-Bessel differential operator are studied. The article investigates the properties of functions given in the form of these potentials. Local integral characteristics are used in the terms, and inequalities are established based on evaluations made in these terms. The weight functions used in the inequalities are treated as if they are monotonic functions. The obtained results are also true for classical harmonic analysis.

References

Abdullayev S.K., Babayev A.A. Some estimates for a singular integral with summable density// DAN SSSR, 1969, v.188, №2, p.263-265.

Abdullayev S.K. On some classes of integral operators in spaces of summable functions // DAN SSSR, 1985, v.283, №4, p.777-780.

Abdullayev S.K., Karamaliyev N.R. Weighed estimates of singular, weakly singular integrals, maximum and fractional maximum functions associated with generalized shift// Proc. of the IV intern. Symposium «Fourier series and their applications», Rostov-na-Donu, 28 may – 3 june, 2006, p.44-52.

Levitan B.M. Expansion in series by Bessel functions, and Fourier integrals. Uspekhi Mat. Nauk, 6 (1951), no. 2, 102-143 pp.

S. K. Abdullayev, E.А.Mammadov. Sobolev-Il'in Inequality for a Class of Generalized Shift Subadditive Operators Nonlinear Analysis and Diferential Equations, Vol.5, 2017, no. 2, 75 - 88

S.K.Abdullayev, R.A.Gadjieva, E.I.Kurbanova. On one variant of Sobolevs theorem / Proc. of the republ. Scientific confer. “Mathematics, mechanics and their applications” dedicated to the 98-th anniversary of the leader of Azerbaijan peorpe H.Aliyev, 24-25 may, p. 110-112 Baku-2021.

S.K.Abdullayev,E.А.Mammadov Integral operators of harmonic analysis is spaces determined in terms of local characteristic functions. International Journal of Pure and Applied Mathematics, v.114-3, 2017, 65-73.

B.K.Agarzayev. Weight analogs of Sobolevs second theorem for Riesz potentials// Vestnik of Baku univ. ser. phys.-math. sc. , 2013, №4, p.86-95.

S.K. Abdullayev, E.A. Mammedov "On one class of subadditive operators with generalized shift" Ukrainskyi Mathmatychnyi Zhurnal 72 (1), 3-19, 2020

Abdullaev S.K., Gadzhieva R.O., Mammadov G.V. "Some tasks of Fourier-Bessel harmonic analysis", Baku, 2021

Downloads

Published

2024-06-03

How to Cite

Bahruz Agarzayev, Mirzayeva, G., Aynur Abdullayeva, Gojayeva Khadija, & Bagirova Sabira. (2024). WEIGHTED INEQUALITIES FOR THE TRACES OF FUNCTIONS REPRESENTED BY THE RIESZ GENERALIZED POTENTIALS. Results in Nonlinear Analysis, 7(2), 154–159. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/366