37 research outputs found
a decomposition of the dual space of some banach function spaces
We give a decomposition for the dual space of some Banach Function Spaces as the Zygmund space of the exponential integrable functions, the Marcinkiewicz space , and the Grand Lebesgue Space
Characterization of interpolation between Grand, small or classical Lebesgue spaces
In this paper, we show that the interpolation spaces between Grand, small or
classical Lebesgue are so called Lorentz-Zygmund spaces or more generally
-spaces. As a direct consequence of our results any Lorentz-Zygmund
space , is an interpolation space in the sense of
Peetre between either two Grand Lebesgue spaces or between two small spaces
provided that . The method consists in computing
the so called K-functional of the interpolation space and in identifying the
associated norm
Norm estimates in Grand Lebesgue Spaces for some operators, including magic square matrices
We extend the classical Lebesgue-Riesz norm estimations for integral
operators acting between different classical Lebesgue-Riesz spaces into the
Grand Lebesgue Spaces, in the general case. As an example we consider matrix
operators acting between finite dimensional Lebesgue-Riesz spaces, especially
generated by means of positive magic squares
Bochner-Riesz operators in Grand Lebesgue spaces
We provide the conditions for the boundedness of the Bochner-Riesz operator
acting between two different Grand Lebesgue Spaces. Moreover we obtain a lower
estimate for the constant appearing in the Lebesgue-Riesz norm estimation of
the Bochner-Riesz operator and we investigate the convergence of the
Bochner-Riesz approximation in Lebesgue-Riesz spaces