Two new mappings associated with inequalities of Hadamard-type for convex functions.
We generalize a well-known separation condition of Everitt and Giertz to a class of weighted symmetric partial differential operators defined on domains in . Also, for symmetric second-order ordinary differential operators we show that where is a singular point guarantees separation of on its minimal domain and extend this criterion to the partial differential setting. As a particular example it is shown that is separated on its minimal domain if is superharmonic. For the criterion...
In this paper, we give a generalization of Fefferman-Stein inequality for the fractional one-sided maximal operator: where and . We also obtain a substitute of dual theorem and weighted norm inequalities for the one-sided fractional integral .
New sufficient conditions on the weight functions u(.) and v(.) are given in order that the fractional maximal [resp. integral] operator Ms [resp. Is], 0 ≤ s < n, [resp. 0 < s < n] sends the weighted Lebesgue space Lp(v(x)dx) into Lp(u(x)dx), 1 < p < ∞. As a consequence a characterization for this estimate is obtained whenever the weight functions are radial monotone.
Let s* denote the maximal function associated with the rectangular partial sums of a given double function series with coefficients . The following generalized Hardy-Littlewood inequality is investigated: , where ξ̅=max(ξ,1), 0 < p < ∞, and μ is a suitable positive Borel measure. We give sufficient conditions on and μ under which the above Hardy-Littlewood inequality holds. Several variants of this inequality are also examined. As a consequence, the ||·||p,μ-convergence property of ...
Necessary and sufficient conditions governing two-weight norm estimates for multiple Hardy and potential operators are presented. Two-weight inequalities for potentials defined on nonhomogeneous spaces are also discussed. Sketches of the proofs for most of the results are given.