Under weak conditions on the kernels, we obtain sharp Lp bounds for rough parabolic maximal integral operators over surfaces of revolution. By virtue these along with Yano’s extrapolation argument, confirm boundedness under weaker kernels. Our obtained results represent substantial extensions and improvements some known kernels symmetric spaces.

Supplying the missing necessary conditions, we complete characterisation of Lp→Lq boundedness commutators [b,T] pointwise multiplication and Calderón–Zygmund operators, for arbitrary pairs 1<p,q<∞ under minimal non-degeneracy hypotheses on T. For p≤q (and especially p=q), this extends a long line results more restrictive assumptions In particular, answer recent question Lerner, Ombrosi, Rivera-...

In this paper, we establish certain Lp bounds for several classes of rough Marcinkiewicz integrals over surfaces revolution on product spaces. By using these and an extrapolation argument, obtain the boundedness under very weak conditions kernel functions. Our results represent natural extensions improvements known integrals.

The operators obtained by taking conditional expectation of continuous time martingale transforms are studied, both on the circle T and on R". Using a Burkholder-Gundy inequality for vector-valued martingales, it is shown that the vector formed by any number of these operators is bounded on LP(R"), 1 < p < oo, with constants that depend only on p and the norms of the matrices involved. As a cor...

According to Steckin [4], the operator F on lp is bounded for every fixed p > 1, that is, (4) and (5) imply that y exists and is in lp and that (6) ||y||, ^ Const. ||*||,. Furthermore, the norm \\f\\p of F (that is, the least Const, satisfying (6)) is subject to an inequality of the type (7) \\F(f)\\P = 5,11/H, where Bp is an absolute constant, depending only on p. In what follows, p > 1 is fix...

We prove Lp estimates of a class generalized Marcinkiewicz integral operators with mixed homogeneity on product domains. By using these along an extrapolation argument, we obtain the boundedness our under very weak conditions kernel functions. Our results in this paper improve and extend several known both integrals parabolic

In this paper, we prove that the weighted BMO space $${\rm{BM}}{{\rm{O}}^p}(\omega ) = \left\{ {f \in L_{{\rm{loc}}}^1:\mathop {\sup }\limits_Q \left\| {{\chi _Q}} \right\|_{{L^p}(\omega )}^{ - 1}{{\left\| {(f {f_Q}){\omega ^{ 1}}{\chi \right\|}_{{L^p}(\omega )}} < \infty } \right\}$$ is independent of scale p ∈ (0, ∞) in sense norm when ω A1. Moreover, can replace Lp(ω) by Lp,∞(ω). As an appli...