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Start Over Creator Gogatishvili, Amiran

1. Compact embeddings of Besov spaces involving only slowly varying smoothness

Creator:
Caetano, Antonio, Gogatishvili, Amiran, and Opic, Bohumír
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Besov spaces with generalized smoothness, Lorentz-Karamata spaces, and compact embeddings
Language:
English
Description:
We characterize compact embeddings of Besov spaces $B^{0,b}_{p,r}(\mathbb {R}^n)$ involving the zero classical smoothness and a slowly varying smoothness $b$ into Lorentz-Karamata spaces $L_{p, q; \bar {b}}(\Omega )$, where $\Omega $ is a bounded domain in $\mathbb {R}^n$ and $\bar {b}$ is another slowly varying function.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Dual spaces of local Morrey-type spaces

Creator:
Gogatishvili, Amiran and Mustafayev, Rza
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
local Morrey-type spaces, complementary local Morrey-type spaces, associated spaces, dual spaces, and multidimensional reverse Hardy inequalities
Language:
English
Description:
In this paper we show that associated spaces and dual spaces of the local Morrey-type spaces are so called complementary local Morrey-type spaces. Our method is based on an application of multidimensional reverse Hardy inequalities.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Embeddings between weighted Copson and Cesàro function spaces

Creator:
Gogatishvili, Amiran, Mustafayev, Rza, and Ünver, Tuğçe
Format:
print, bez média, and svazek
Type:
model:article and TEXT
Subject:
matematika, mathematics, Cesàro and Copson function spaces, embedding, iterated Hardy inequalities, 13, and 51
Language:
English
Description:
In this paper, characterizations of the embeddings between weighted Copson function spaces ${\rm Cop}_{p_1,q_1}(u_1,v_1)$ and weighted Cesàro function spaces ${\rm Ces}_{p_2,q_2}(u_2,v_2)$ are given. In particular, two-sided estimates of the optimal constant $c$ in the inequality $ \align\biggl( \int_0^{\infty} &\biggl( \int_0^t f(\tau)^{p_2}v_2(\tau)\dd\tau\biggr)^{\!\!\frc{q_2}{p_2}} u_2(t)\dd t\biggr)^{\!\!\frc1{q_2}} $ \ $\le c \biggl( \int_0^{\infty} \biggl( \int_t^{\infty} f(\tau)^{p_1} v_1(\tau)\dd\tau\biggr)^{\!\!\frc{q_1}{p_1}} u_1(t)\dd t\biggr)^{\!\!\frc1{q_1}}, $ 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 $(0,\infty)$, are obtained. The most innovative part consists of the fact that possibly different parameters $p_1$ and $p_2$ and possibly different inner weights $v_1$ and $v_2$ are allowed. The proof is based on the combination of duality techniques with estimates of optimal constants of the embeddings between weighted Cesàro and Copson spaces and weighted Lebesgue spaces, which reduce the problem to the solutions of iterated Hardy-type inequalities., Amiran Gogatishvili, Rza Mustafayev, Tuğçe Ünver., and Obsahuje bibliografii
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

4. Normability of Lorentz spaces—an alternative approach

Creator:
Gogatishvili, Amiran and Soudský, Filip
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
weighted Lorentz space, weighted inequality, non-increasing rearrangement, Banach function space, and associate space
Language:
English
Description:
We study normability properties of classical Lorentz spaces. Given a certain general lattice-like structure, we first prove a general sufficient condition for its associate space to be a Banach function space. We use this result to develop an alternative approach to Sawyer's characterization of normability of a classical Lorentz space of type $\Lambda $. Furthermore, we also use this method in the weak case and characterize normability of $\Lambda _{v}^{\infty }$. Finally, we characterize the linearity of the space $\Lambda _{v}^{\infty }$ by a simple condition on the weight $v$.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public