In this paper, a good λ estimate for the multilinear commutator associated to the fractional integral operator on the spaces of homogeneous type is obtained. Under this result, we get the(Lp(X),Lq(X)) -boundedness of the multilinear commutator. Mathematics subject classification (2010): 42B20, 42B25.

We consider the problem of bounding the expected value of a linear program (LP) containing random coe&cients, with applications to solving two-stage stochastic programs. An upper bound for minimizations is derived from a restriction of an equivalent, penalty-based formulation of the primal stochastic LP, and a lower bound is obtained from a restriction of a reformulation of the dual. Our “restr...

Abstract: In this paper we consider Lp boundedness of some commutators of Riesz transforms associated to Schrödinger operator P = −∆+ V (x) on Rn, n ≥ 3. We assume that V (x) is non-zero, nonnegative, and belongs to Bq for some q ≥ n/2. Let T1 = (−∆ + V ) −1V, T2 = (−∆ + V )−1/2V 1/2 and T3 = (−∆+ V ) −1/2∇. We obtain that [b, Tj ] (j = 1, 2, 3) are bounded operators on Lp(Rn) when p ranges in ...

In this paper we give sufficient conditions on pair of weights (w, v) for some one-sided operators to be bounded from Lp(vp) to Lp(wp). The operators we deal with include the one-sided fractional maximal operator and the one-sided singular integrals. For the first operator necessary and sufficient conditions are knwon (see [MT], [LT]). These conditions usually amount to check the boundedness of...

New conditions of Lp[0,∞)−Lq[0,∞) boundedness and compactness for the operator f → w(x) R b(x) a(x) k(x, y)f(y)v(y)dy with locally integrable weight functions v, w and a positive continuous kernel k(x, y) from Oinarov’s type class are obtained for 1 < p, q <∞.

Conditions sufficient for boundedness of the Bergman type operators on certain mixed norm spaces Lp,q(φ) (0 < p < 1, 1 < q <∞) of functions on the unit ball of Cn are given, and this is used to solve Gleason’s problem for the mixed norm spaces Hp,q(φ) (0 < p < 1, 1 < q <∞).

Abstract. Let L be an elliptic differential operator with bounded measurable coefficients, acting in Bochner spaces Lp(Rn;X) of X-valued functions on Rn. We characterize Kato’s square root estimates ‖ √ Lu‖p h ‖∇u‖p and the H-functional calculus of L in terms of R-boundedness properties of the resolvent of L, when X is a Banach function lattice with the UMD property, or a noncommutative Lp spac...

We study Fredholmness of nonlocal boundary value problems for fourth order elliptic differential-operator equations in UMD Banach spaces. The main condition is given in terms of R-boundedness of some families of bounded operators generated by inverse of the characteristic operator pencil of the equation. Then we prove an isomorphism of the problem on the semi-axis, for some special boundary con...

The aim of this paper is to establish the vector-valued inequalities for Littlewood-Paley operators, including the Lusin area integrals, the Littlewood-Paley g-functions and g∗μ-functions, and their commutators on the Herz-Morrey spaces with variable exponentMK̇ p,q(·)(R n). By applying the properties of Lp(·)(Rn) spaces and the vector-valued inequalities for Littlewood-Paley operators and their...