We define for 1 <= r < infinity a norm for the class of functions which are Henstock-Kurzweil integrable in the L-r sense. We then establish that the dual in this norm is isometrically isomorphic to L-r' and is therefore a Banach space, and in the case r = 2, a Hilbert space. Finally, we give results pertaining to convergence and weak convergence in this space.

Musial, P., & Tulone, F. (2019). Dual of the Class of HKr Integrable Functions. MINIMAX THEORY AND ITS APPLICATIONS, 4(1), 151-160.

Dual of the Class of HKr Integrable Functions

Tulone, F
2019

Abstract

We define for 1 <= r < infinity a norm for the class of functions which are Henstock-Kurzweil integrable in the L-r sense. We then establish that the dual in this norm is isometrically isomorphic to L-r' and is therefore a Banach space, and in the case r = 2, a Hilbert space. Finally, we give results pertaining to convergence and weak convergence in this space.
Settore MAT/05 - Analisi Matematica
Musial, P., & Tulone, F. (2019). Dual of the Class of HKr Integrable Functions. MINIMAX THEORY AND ITS APPLICATIONS, 4(1), 151-160.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/423776
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