Related papers: Weighted Inequalities for One-sided Fractional Min…
We study two weight norm inequalities for a vector-valued operator from a weighted $L^p(\sigma)$-space to mixed norm $L^q_{l^s}(\mu)$ spaces, $1<q<p$. We apply these results to the boundedness of Wolff's potentials.
In this paper, we prove analogues of O'Neil's inequalities for the convolution in the weighted Lebesgue spaces. We also establish the weighted two-sided norm inequalities for the potential operator.
In this article, we investigate the weighted $m-$subharmonic functions. We shall give some properties of this class and consider its relation to the $m-$Cegrell classes. We also prove an integration theorem and an almost everywhere…
We obtain sharp inequalities for the k-plane transform, the "j-plane to k-plane" transform, and the corresponding dual transforms, acting on $L^p$ spaces with a radial power weight. The operator norms are explicitly evaluated. Some…
Let $f$ be a measurable function defined on $\mathbb{R}$. For each $n\in\mathbb{Z}$ define the operator $A_n$ by $$A_nf(x)=\frac{1}{2^n}\int_x^{x+2^n}f(y)\, dy.$$ Consider the variation operator…
In this article we introduce the fractional Hardy-Littlewood maximal function on the infinite rooted $k$-ary tree and study its weighted boundedness. We also provide examples of weights for which the fractional Hardy-Littlewood maximal…
We introduce and study weak o-minimality in the context of complete types in an arbitrary first-order theory. A type $p\in S(A)$ is weakly o-minimal if for some relatively $A$-definable linear order, $<$, on $p(\mathfrak{C})$ every…
In this paper we discuss the structure of weighted weak Lebesgue spaces and weighted weak Orlicz spaces on $\mathbb{R}^n$. First, we present sufficient and necessary conditions for inclusion relation between weighted weak Lebesgue spaces.…
Some mathematical inequalities among various weighted means are studied. Inequalities on weighted logarithmic mean are given. Besides, the gap in Jensen's inequality is studied as a convex function approach. Consequently, some non-trivial…
We give a classification between weighted norm inequalities of strong fractional integral operators, and their associated multi-parameter Muckenhoupt characteristics, bu considering the weights to be power functions. As a result, we extend…
Let $ Tf =\sum_{ I} \varepsilon_I \langle f,h_{I^+}\rangle h_{I^-}$. Here, $ \lvert \varepsilon _I\rvert=1 $, and $ h_J$ is the Haar function defined on dyadic interval $ J$. We show that, for instance, \begin{equation*} \lVert T \rVert _{L…
The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. In this paper, we establish a number of simple inequalities for the weighted entropies…
Two classes of fractional type variable weights are established in this paper. The first kind of weights ${A_{\vec p( \cdot ),q( \cdot )}}$ are variable multiple weights, which are characterized by the weighted variable boundedness of…
We prove the endpoint weak type estimate for square functions of Marcinkiewicz type with fractional integrals associated with non-isotropic dilations. This generalizes a result of C. Fefferman on functions of Marcinkiewicz type by…
In this paper, we give more general definitions of weighted means and MN-convex functions. Using these definitions, we also obtain some generalized results related to properties of MN-convex functions. The importance of this study is that…
The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp boundsare obtained for both the fractional integral operators and the…
In the context of variable exponent Lebesgue spaces equipped with a lower Ahlfors measure we obtain weighted norm inequalities over bounded domains for the centered fractional maximal function and the fractional integral operator.
The operators of fractional calculus come in many different types, which can be categorised into general classes according to their nature and properties. We conduct a formal study of the class known as weighted fractional calculus and its…
In this article, we introduce the fractional maximal operator on the Hyperbolic space, a non-doubling measure space, and study the weighted boundedness. Motivated in the weighted boundedness of Hardy-Littlewood maximal studied by Antezana…
For a wide range of pairs of mixed norm spaces such that one space is contained in another, we characterize all cases when contractive norm inequalities hold. In particular, this yields such results for many pairs of weighted Bergman…