arXiv subjects

Nino Samashvili

Publications and source records attributed to Nino Samashvili.

3 recordsLinked to original sources

arXiv2020

divergent Fourier series in function spaces near $L^1[0;1]$

In this paper we generalize Bochkariev's theorem, which states that for any uniformly bounded orthonormal system $Φ$, there exists a Lebesgue integrable function such that the Fourier series of it with respect to system $Φ$ diverge on the set of positive measure. We characterize the class of variable exponent Lebesgue spaces $L^{p(\cdot)}[0;1]$, $1<p(x)<\infty$ a.e. on [0;1], such that above mentioned Bochkarev's theorem is valid.

math.FA↗

arXiv2015

Some $s$-numbers of an integral operator of Hardy type in Banach function spaces

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 0$ depend only on the space $E.$

math.FA↗

arXiv2014

On the upper and lower estimates of norms in variable exponent spaces

In the present paper we investigate some geometrical properties of the norms in Banach function spaces. Particularly there is shown that if exponent $1/p(\cdot)$ belongs to $BLO^{1/\log}$ then for the norm of corresponding variable exponent Lebesgue space we have the following lower estimate $$\left\|\sum χ_{Q}\|fχ_{Q}\|_{p(\cdot)}/\|χ_{Q}\|_{p(\cdot)}\right\|_{p(\cdot)}\leq C\|f\|_{p(\cdot)}$$ where $\{Q\}$ defines disjoint partition of $[0;1]$. Also we have constructed variable exponent Lebesgue space with above property which does not possess following upper estimation $$\|f\|_{p(\cdot)}\leq C\left\|\sum χ_{Q}\|fχ_{Q}\|_{p(\cdot)}/\|χ_{Q}\|_{p(\cdot)}\right\|_{p(\cdot)}. $$

math.FA↗