An Investigation In The Inclucion Theorem Which Related To Lorentz Spaces
Abstract
In this paper, we studied a problem at functional analysis, it is the inclusion of function spaces, especially we studied the inclusion between Lorentz space type (r,p,q), In the beginning, we introduced this space and then, we studied some of its basic properties where we proved that it is non-empty, linear, quasi-normed and complete space, then we proved the inclusion of this space for different cases of the parameters, First for1≤q_1≤q_2<∞ , then for 0≤r_2≤r_1<∞ ,
after that for 0≤r_2≤r_1<∞ & و1≤q_1≤q_2<∞ at the same time.
In addition to some other inclusion cases.
Then, we proved one of the cases of inclusion between these spaces and bounded stummel modulus classes type (r, q,α).
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