On some integral operators on weighted Hardy spaces

V.M.Dilnyi

We consider an intermediate, in some sense, space of functions between $L^p, p> 1,$ and the Hardy space $H^1 $. For this space, it is shown boundedness of one class of integral operators.

1. Koosis P. Introduction to $H^p$ spaces, Sec. ed. -- Cambridge Tracts in Mathematics, V.115. -- Cambridge: Cambridge University Press, 1998.

2. Vinnitskii B. On zeros of functions analytic in a half plane and completeness of systems of exponents, Ukr. Math. J. 46 (1994), 484--500 (Ukrainian).

3. Седлецкий А. М. Эквивалентное определение пространств $H^p$ в полуплоскости и некоторые приложения, Матем. сб. 96 (1975), № 1, 75–82.

4. Phong D. H., Stein E.~M. Hilbert integrals, singular integrals and Radon transforms, I, Acta Math. 157 (1987), 179--194.

5. Sampson G. Oscillatory kernels that map $H^1$ into $L^1$, Arkiv f\"or Matematik, 18 (1980), 125--144.

6. Pan Y. Hardy spaces and oscillatory singular integrals: II, Pacific Journ. of Math. 168 (1995), 167--182.

7. Vynnytskyi B., Dil'nyi V. On an analogue of Paley-Wiener's theorem for weighted Hardy spaces, Mat. Stud. 14 (2000), 35--40 (Ukrainian).

8. Vynnytskyi B., Dil'nyi V. On extension of Beurling-Lax theorem, Math. Notes, 79 (2006), 362--368. (Russian)

9. Kantorovich L., Akilov G. Functional analysis, Nauka, Moscow, 1977, Pergamon Press, Oxford, 1982.

10. Vynnytskyi B., Dil'nyi V. On Cauchy and Poisson type formulas for one weighted Hardy space, Mat. Stud. 28 (2007), 209--212 (Ukrainian).

11. Vynnytskyi B. On zeros of some classes of functions analytic in half-plane, Mat. Stud. 6 (1996), 67--72. (Ukrainian)

12. Pan Y. Oscillatory singular integrals on $L^p$ and Hardy Spaces, Proc. Amer. Math. Soc. 124 (1996), 2821--2825.

	On some integral operators on weighted Hardy spaces
Author	V.M.Dilnyi dilnyi@ukr.net Drohobych Ivan Franko State University,Institute of Physics, Mathematics and Informatics
Abstract	We consider an intermediate, in some sense, space of functions between $L^p, p> 1,$ and the Hardy space $H^1 $. For this space, it is shown boundedness of one class of integral operators.
Keywords	integral operator, weighted Hardy space, boundedness
DOI	doi:10.30970/ms.31.1.107-112
Reference	1. Koosis P. Introduction to $H^p$ spaces, Sec. ed. -- Cambridge Tracts in Mathematics, V.115. -- Cambridge: Cambridge University Press, 1998. 2. Vinnitskii B. On zeros of functions analytic in a half plane and completeness of systems of exponents, Ukr. Math. J. 46 (1994), 484--500 (Ukrainian). 3. Седлецкий А. М. Эквивалентное определение пространств $H^p$ в полуплоскости и некоторые приложения, Матем. сб. 96 (1975), № 1, 75–82. 4. Phong D. H., Stein E.~M. Hilbert integrals, singular integrals and Radon transforms, I, Acta Math. 157 (1987), 179--194. 5. Sampson G. Oscillatory kernels that map $H^1$ into $L^1$, Arkiv f\"or Matematik, 18 (1980), 125--144. 6. Pan Y. Hardy spaces and oscillatory singular integrals: II, Pacific Journ. of Math. 168 (1995), 167--182. 7. Vynnytskyi B., Dil'nyi V. On an analogue of Paley-Wiener's theorem for weighted Hardy spaces, Mat. Stud. 14 (2000), 35--40 (Ukrainian). 8. Vynnytskyi B., Dil'nyi V. On extension of Beurling-Lax theorem, Math. Notes, 79 (2006), 362--368. (Russian) 9. Kantorovich L., Akilov G. Functional analysis, Nauka, Moscow, 1977, Pergamon Press, Oxford, 1982. 10. Vynnytskyi B., Dil'nyi V. On Cauchy and Poisson type formulas for one weighted Hardy space, Mat. Stud. 28 (2007), 209--212 (Ukrainian). 11. Vynnytskyi B. On zeros of some classes of functions analytic in half-plane, Mat. Stud. 6 (1996), 67--72. (Ukrainian) 12. Pan Y. Oscillatory singular integrals on $L^p$ and Hardy Spaces, Proc. Amer. Math. Soc. 124 (1996), 2821--2825.
Pages	107-112
Volume	31
Issue	1
Year	2009
Journal	Matematychni Studii
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