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The n -dual space of the space of p -summable sequences

Yosafat E. P. Pangalela;  Hendra Gunawan — 2013

Mathematica Bohemica

In the theory of normed spaces, we have the concept of bounded linear functionals and dual spaces. Now, given an n -normed space, we are interested in bounded multilinear n -functionals and n -dual spaces. The concept of bounded multilinear n -functionals on an n -normed space was initially intoduced by White (1969), and studied further by Batkunde et al., and Gozali et al. (2010). In this paper, we revisit the definition of bounded multilinear n -functionals, introduce the concept of n -dual spaces, and...

Norm estimates for Bessel-Riesz operators on generalized Morrey spaces

Mochammad Idris;  Hendra Gunawan;  A. Eridani — 2018

Mathematica Bohemica

We revisit the properties of Bessel-Riesz operators and present a different proof of the boundedness of these operators on generalized Morrey spaces. We also obtain an estimate for the norm of these operators on generalized Morrey spaces in terms of the norm of their kernels on an associated Morrey space. As a consequence of our results, we reprove the boundedness of fractional integral operators on generalized Morrey spaces, especially of exponent 1 , and obtain a new estimate for their norm.

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