Basic questions concerning nonsingular multilinear operators with oscillatory factors are posed and partially answered. L norm inequalities are established for multilinear integral operators of Calderón-Zygmund type which incorporate oscillatory factors e iP , where P is a real-valued polynomial. A related problem concerning upper bounds for measures of sublevel sets is solved.

We obtain an alternative approach to recent results by M. Lacey and Hytönen–Roncal–Tapiola about a pointwise domination of ω-Calderón–Zygmund operators by sparse operators. This approach is rather elementary and it also works for a class of nonintegral singular operators.

Boundedness results for bilinear square functions and vector-valued operators on products of Lebesgue, Sobolev, and other spaces of smooth functions are presented. Bilinear vector-valued Calderón-Zygmund operators are introduced and used to obtain bounds for the optimal range of estimates in target Lebesgue spaces including exponents smaller than one.

To study the compactness of bilinear commutators certain Calderón–Zygmund operators which include (inhomogeneous) Coifman–Meyer Fourier multipliers and pseudodifferential as special examples, Torres Xue (Rev Mat Iberoam 36:939–956, 2020) introduced a new subspace BMO $$\,(\mathbb {R}^n)$$ , denoted by XMO conjectured that it is just space VMO D. Sarason. In this article, authors give negative a...

In this paper we extend an inequality of Littlewood concerning the higher variations of functions of bounded Fréchet variations of two variables (bimeasures) to a class of functions that are p-bimeasures, by using the machinery of vector measures. Using random estimates of Kahane-Salem-Zygmund, we show that the inequality is sharp.

It is shown that the Lw,1< p<∞, operator norms of Littlewood–Paley operators are bounded by a multiple of ‖w‖ Ap , where γp = max{1, p/2} 1 p−1 . This improves previously known bounds for all p > 2. As a corollary, a new estimate in terms of ‖w‖Ap is obtained for the class of Calderón–Zygmund singular integrals commuting with dilations.

ABSTRACT: In this paper, the complete convergence and the complete moment convergence of weighted sums for an array of negatively superadditive dependent random variables are established. The results generalize the Baum-Katz theorem on negatively superadditive dependent random variables. In particular, the Marcinkiewicz-Zygmund type strong law of large numbers of weights sums for sequences of n...

Convolution type Calderón-Zygmund singular integral operators with rough kernels p.v. Ω(x)/|x| are studied. A condition on Ω implying that the corresponding singular integrals and maximal singular integrals map L → L for 1 < p < ∞ is obtained. This condition is shown to be different from the condition Ω ∈ H1(Sn−1).

We obtain Calderón-Zygmund estimates for some degenerate equations of Kolmogorov type with inhomogeneous nonlinear coefficients. We then derive the well-posedness of the martingale problem associated with related degenerate operators, and therefore uniqueness in law for the corresponding stochastic differential equations. Some density estimates are established as well.

In this paper, we obtain some characterizations of the boundedness and compactness of the products of the radial derivative and multiplication operator RMu between mixed norm spaces H(p, q, φ) and Zygmund-type spaces on the unit ball. Mathematics subject classification (2010): 47B38, 47G10, 32A10, 32A18.