We obtain sharp weighted Lp estimates in the Rubio de Francia extrapolation theorem in terms of the Ap characteristic constant of the weight. Precisely, if for a given 1 < r < âˆž the norm of aâ€¦ (More)

Ïƒ1[x] Â· Ïƒ2[x]. Therefore, if we find s > 0 such that Ïƒ[x] < 0 for some x satisfying Ïƒ2[x]/Ïƒ1[x] = s 2, we get a contradiction with (1.1). Consider the set S âŠ‚ (0,âˆž) Ã— (0,âˆž) consisting of all pairsâ€¦ (More)

Estimation of L norms of Fourier multipliers is known to be hard. It is usually connected to some interesting types of PDE, see several such PDE for several Fourier multipliers on the line in aâ€¦ (More)

We prove a bilinear embedding theorem for SchrÃ¶dinger operators with nonnegative potentials. The embedding, acting on the cartesian product of L(R) and its dual, involves estimates that areâ€¦ (More)

The main aspiration of this note is to construct several different Haar-type systems in euclidean spaces of higher dimensions and prove sharp Lp bounds for the corresponding martingale transforms. Inâ€¦ (More)

Let LA, LB be the operators in divergence form associated with complex uniformly accretive matrix functions A,B on R. Take p > 1 and assume that for a.e. x âˆˆ R we have Re ã€ˆA(x)Î¾, JpÎ¾ã€‰ > Cp|Î¾| 2 forâ€¦ (More)

We utilize the Bellman function technique to prove a bilinear dimension-free inequality for the Hermite operator. The Bellman technique is applied here to a non-local operator, which at first did notâ€¦ (More)