Generalized Morrey spaces associated to Schrödinger operators and applications

Trong, Nguyen Ngoc; Trường, Lê Xuân

doi:10.21136/cmj.2018.0039-17

Cited by 6 publications

(1 citation statement)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Definition 1.4. ( [26]) Suppose that u, w are two weights, λ ∈ [0, 1), 1 ≤ p < l ≤ ∞, α ∈ (−∞, ∞), and Q := Q(z, r). The strong Morrey space M p,l α,λ (u, w) consists of any measurable function f satisfying ∥f ∥ M p,l α,λ (u,w) < ∞, where…”

Section: Introductionmentioning

confidence: 99%

Sharp maximal estimates for multilinear commutators of multilinear strongly singular Calderón–Zygmund operators and applications

Lin

2018

Forum Mathematicum

View full text Add to dashboard Cite

In this paper, we aim to establish the sharp maximal pointwise estimates for the multilinear commutators generated by multilinear strongly singular Calderón–Zygmund operators and BMO functions or Lipschitz functions, respectively. As applications, the boundedness of these multilinear commutators on product of weighted Lebesgue spaces are obtained. It is interesting to note that there is no size condition assumption for the kernel of the multilinear strongly singular Calderón–Zygmund operator. Due to the stronger singularity for the kernel of the multilinear strongly singular Calderón–Zygmund operator, we need to be more careful in estimating the mean oscillation over the small balls to get the sharp maximal function estimates.

show abstract

Section: Introductionmentioning

confidence: 99%