$\left( L^{p} ,L^{q} \right)$ Properties of the Potential-Type Integrals Associated to Non-doubling Measures

Authors

  • Mubariz G. Hajibayov Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan

DOI:

https://doi.org/10.5644/SJM.02.2.05

Keywords:

Riesz potentials, generalized potential-type integrals, nondoubling measures

Abstract

The $\left( L^{p} ,L^{q} \right) $ boundedness of the potential-type integrals associated to non-doubling measures are investigated.

 

1991 Mathematics Subject Classification. 31B15, 46E35

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References

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A. D. Gadjiev, On generalized potential-type integral operators, Functiones et Approximatio, UAM, 25 (1997), 37–44.

J. Garcia-Cuerva and A. E. Gatto, Boundedness properties of fractional operators associated to non-doubling measures, Stud. Math., 162 (3) (2004), 245–261.

V. Kokilashvili and A. Meskhi, Fractional integrals on measure spaces, Frac. Calc. Appl. Anal., 4 (1) (2001), 1–24.

E. Nakai, On generalized fractional integrals, Taiwanese J. Math., 5 (3) (2001), 587–602.

E. Nakai and H. Sumitomo, On generalized Riesz potentials and spaces of some smooth functions, Sci. Math. Japonicae, 54 (3) (2001), 463–472.

E. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton, 1970.

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Published

12.06.2024

How to Cite

Hajibayov, M. G. (2024). $\left( L^{p} ,L^{q} \right)$ Properties of the Potential-Type Integrals Associated to Non-doubling Measures. Sarajevo Journal of Mathematics, 2(2), 173–180. https://doi.org/10.5644/SJM.02.2.05

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