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Two separation criteria for second order ordinary or partial differential operators

Richard C. Brown, Don B. Hinton (1999)

Mathematica Bohemica

We generalize a well-known separation condition of Everitt and Giertz to a class of weighted symmetric partial differential operators defined on domains in n . Also, for symmetric second-order ordinary differential operators we show that lim sup t c ( p q ' ) ' / q 2 = θ < 2 where c is a singular point guarantees separation of - ( p y ' ) ' + q y on its minimal domain and extend this criterion to the partial differential setting. As a particular example it is shown that - Δ y + q y is separated on its minimal domain if q is superharmonic. For n = 1 the criterion...

Two weight norm inequalities for fractional one-sided maximal and integral operators

Liliana De Rosa (2006)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we give a generalization of Fefferman-Stein inequality for the fractional one-sided maximal operator: - + M α + ( f ) ( x ) p w ( x ) d x A p - + | f ( x ) | p M α p - ( w ) ( x ) d x , where 0 < α < 1 and 1 < p < 1 / α . We also obtain a substitute of dual theorem and weighted norm inequalities for the one-sided fractional integral I α + .

Two weight norm inequality for the fractional maximal operator and the fractional integral operator.

Yves Rakotondratsimba (1998)

Publicacions Matemàtiques

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 &lt; n, [resp. 0 &lt; s &lt; n] sends the weighted Lebesgue space Lp(v(x)dx) into Lp(u(x)dx), 1 &lt; p &lt; ∞. As a consequence a characterization for this estimate is obtained whenever the weight functions are radial monotone.

Two-parameter Hardy-Littlewood inequality and its variants

Chang-Pao Chen, Dah-Chin Luor (2000)

Studia Mathematica

Let s* denote the maximal function associated with the rectangular partial sums s m n ( x , y ) of a given double function series with coefficients c j k . The following generalized Hardy-Littlewood inequality is investigated: | | s * | | p , μ C p , α , β Σ j = 0 Σ k = 0 ( j ̅ ) p - α - 2 ( k ̅ ) p - β - 2 | c j k | p 1 / p , where ξ̅=max(ξ,1), 0 < p < ∞, and μ is a suitable positive Borel measure. We give sufficient conditions on c j k 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 s m n ( x , y ) ...

Two-weighted criteria for integral transforms with multiple kernels

Vakhtang Kokilashvili, Alexander Meskhi (2006)

Banach Center Publications

Necessary and sufficient conditions governing two-weight L p 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.

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