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A. Gogatishvili

Publications and source records attributed to A. Gogatishvili.

4 recordsLinked to original sources
arXiv2022

Almost-compact and compact embeddings of variable exponent spaces

Let $Ω$ be an open subset of $\mathbb{R}^{N}$, and let $p,\, q:Ω\rightarrow \left[ 1,\infty \right] $ be measurable functions. We give a necessary and sufficient condition for the embedding of the variable exponent space $L^{p(\cdot )}\left( Ω\right) $ in $L^{q(\cdot )}\left( Ω\right) $ to be almost compact. This leads to a condition on $Ω, \, p$ and $q$ sufficient to ensure that the Sobolev space $W^{1,p(\cdot )}\left( Ω\right) $ based on $L^{p(\cdot )}\left( Ω\right) $ is compactly embedded in $L^{q(\cdot )}\left( Ω\right) ;$ compact embedding results of this type already in the literature are included as special cases.

math.FA↗
arXiv2019

Some new results related to Lorentz G-gamma spaces and interpolation

We compute the K-functional related to some couple of spaces as small or classical Lebesgue space or Lorentz-Marcinkiewicz spaces completing the results of the previous works of the authors. This computation allows to determine the interpolation space in the sense of Peetre for such couple. It happens that the result is always a G-gamma space, since this last space covers many spaces. The motivations of such study are various, among them we wish to obtain a regularity estimate for the so called very weak solution of linear equation in a domain Omega with data in the space of the integrable function with respect to the distance function to the boundary of Omega.

math.AP↗
arXiv2019

Pointwise Multipliers between weighted Copson and Cesàro function spaces

In this paper the solution of the pointwise multiplier problem between weighted Copson function spaces $\operatorname{Cop}_{p_1,q_1}(u_1,v_1)$ and weighted Cesàro function spaces $\operatorname{Ces}_{p_2,q_2}(u_2,v_2)$ is presented, where $p_1,\,p_2,\,q_1,\,q_2 \in (0,\infty)$, $p_2 \le q_2$ and $u_1,\,u_2,\,v_1,\,v_2$ are weights on $(0,\infty)$.

math.FA↗