ONE GENERALIZED H-TRANSFORMATION IN WEIGHT SPACES OF INTEGRATED FUNCTIONS ON A SEMI-AXIS
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Abstract
The properties of one class of generalized H-transformations in weighted spaces of integrable functions on the semi-axis are studied. Conditions for the boundedness and one-to-oneness of the operators of such transformations from one space 
to another are obtained, analogues of the integration formula by parts are proved, various integral representations for the transformations under study are obtained, descriptions of images are given, and formulas for their inversion are derived.
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References
Kilbas, A. A. H-Transforms. Theory and Applications / A. A. Kilbas, M. H. Saigo. – London : Chapman and Hall. CRC Press, 2004. – 401 p.
Килбас, А. А. Обобщенное H-преобразование в весовых пространствах суммируемых функций / А. А. Килбас, Е. К. Щетникович // Весцi НАН Беларусi. Сер. фiз.-мат. навук. – 2004. – № 2. – С. 14–19.
Самко, С. Г. Интегралы и производные дробного порядка и некоторые их приложения / С. Г. Самко, А. А. Килбас, О. И. Маричев. – Минск : Наука и техника, 1987. – 688 с.
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