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of 61
pro vyhledávání: '"Kopaliani, Tengiz"'
We give a sharp sufficient condition on the distribution function, $|\{x\in \Omega :\,p(x)\leq 1+\lambda\}|$, $\lambda>0$, of the exponent function $p(\cdot): \Omega \to [1,\infty)$ that implies the embedding of the variable Lebesgue space $L^{p(\cdo
Externí odkaz:
http://arxiv.org/abs/2406.03392
Autor:
Adamadze, Daviti, Kopaliani, Tengiz
Let $S_{n}f$ be the $n$th partial sum of the Vilenkin-Fourier series of $f\in L^{1}(G).$ For $1
Externí odkaz:
http://arxiv.org/abs/2210.11331
Publikováno v:
In Journal of Mathematical Analysis and Applications
Autor:
Adamadze, Daviti, Kopaliani, Tengiz
Valadier and Hensgen proved independently that the restriction of functional $\phi(x)=\int_{0}^{1}x(t)dt,\,\,x\in L^{\infty}([0,1])$ on the space of continuous functions $C([0,1])$ admits a singular extension back to the whole space $L^{\infty}([0,1]
Externí odkaz:
http://arxiv.org/abs/2004.09901
In this paper we generalize Bochkariev's theorem, which states that for any uniformly bounded orthonormal system $\Phi$, there exists a Lebesgue integrable function such that the Fourier series of it with respect to system $\Phi$ diverge on the set o
Externí odkaz:
http://arxiv.org/abs/2003.07563
The paper introduces a variable exponent space $X$ which has in common with $L^{\infty}([0,1])$ the property that the space $C([0,1])$ of continuous functions on $[0,1]$ is a closed linear subspace in it. The associate space of $X$ contains both the
Externí odkaz:
http://arxiv.org/abs/1710.03990
Autor:
Fiorenza, Aberto, Formica, Maria Rosaria, Gogatishvili, Amiran, Kopaliani, Tengiz, Rakotoson, Jean Michel
In this paper, we show that the interpolation spaces between Grand, small or classical Lebesgue are so called Lorentz-Zygmund spaces or more generally $G\Gamma$-spaces. As a direct consequence of our results any Lorentz-Zygmund space $L^{a,r}({\rm Lo
Externí odkaz:
http://arxiv.org/abs/1709.05892
Publikováno v:
In Journal of Mathematical Analysis and Applications 15 January 2022 505(2)
Let $s_{n}(T)$ denote the $n$th approximation, isomorphism, Gelfand, Kolmogorov or Bernstein number of the Hardy-type integral operator $T$ given by $$ Tf(x)=v(x)\int_{a}^{x}u(t)f(t)dt,\,\,\,x\in(a,b)\,\,(-\infty
Externí odkaz:
http://arxiv.org/abs/1507.08854
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