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We prove that, for every $\alpha > -1$, the pull-back measure $\phi ({\cal A}_\alpha)$ of the measure $d{\cal A}_\alpha (z) = (\alpha + 1) (1 - |z|^2)^\alpha \, d{\cal A} (z)$, where ${\cal A}$ is the...
Some new examples of K-monotone couples of the type (X, X(w)), where X is a symmetric space on [0, 1] and w is a weight on [0, 1], are presented. Based on the property of the w-decomposability of a sy...
We study the homogeneous equation (*) $ u' = \Delta u$, $t > 0$, $u(0)=f\in wX$, where $wX$ is a weighted Banach space, $w(x)= (1+||x||)^k$, $x\in \r^n$ with $k\ge 0$, $ \Delta$ is the Laplacian, $Y$ ...
Using the extrapolation of one-sided weights, we establish the boundedness of commutators generated by weighted Lipschitz functions and one-sided singular integral operators from weighted Lebesgue spa...
Abstract: Let $\Phi$ be a concave function on $(0,\infty)$ of strictly lower type $p_{\Phi}\in(0,1]$ and $\omega\in A^{\mathop\mathrm{loc}}_{\infty}(\mathbb{R}^n)$. We introduce the weighted local Orl...
Abstract: In this paper, we consider localized integral operators whose kernels have mild singularity near the diagonal and certain Holder regularity and decay off the diagonal. Our model example is t...
Abstract: We show how the $A_\infty$ class of weights can be considered as a metric space. As far as we know this is the first time that a metric d is considered on this set. We use this metric to gen...
TheMarcinkiewicz integral is essentially a Littlewood-Paley g-function,which plays a important role in harmonic analysis. In this article, by using the atomic decomposition theory of weighted Hardy sp...
Let ${\mathscr H}$ be a complex seperable Hilbert space and ${\mathscr L}({\mathscr H})$ denote the collection of bounded linear operators on ${\mathscr H}$. For an operator in ${\mathscr L}% ({\maths...
The author presents a modification of the Baskakov operator for the intervals [0,bn], where bn is an increasing sequence of positive numbers with either finite or infinite limit. Convergence propertie...

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