Weighted BMO Type Spaces Associated to Admissible Functions and Applications

Trong, Nguyen Ngoc; Tùng, Nguyễn Thanh

doi:10.1007/s40306-014-0109-5

Cited by 7 publications

(2 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Indeed, the only additional information needed to reproduce the proof of Theorem 5.9 is that the p-power John-Nirenberg estimate for the space BM O * ,w , proved in [29,11], can be extended to BM O * ,w (S). A recent paper by Trong and Tung [36] does exactly this, and hence Theorem 5.9 can also be extended to a space of homogeneous type setting as an application of Theorem 3.2. [18] for the precise condition on T ).…”

Section: 3mentioning

confidence: 78%

John–Nirenberg Inequalities and Weight Invariant BMO Spaces

Hart

Torres

2018

J Geom Anal

View full text Add to dashboard Cite

This work explores new deep connections between John-Nirenberg type inequalities and Muckenhoupt weight invariance for a large class of BM O-type spaces. The results are formulated in a very general framework in which BM O spaces are constructed using a base of sets, used also to define weights with respect to a non-negative measure (not necessarily doubling), and an appropriate oscillation functional. This includes as particular cases many different function spaces on geometric settings of interest. As a consequence the weight invariance of several BM O and Triebel-Lizorkin spaces considered in the literature is proved. Most of the invariance results obtained under this unifying approach are new even in the most classical settings.

show abstract

Section: 3mentioning

confidence: 78%

John–Nirenberg Inequalities and Weight Invariant BMO Spaces

Hart

Torres

2018

J Geom Anal

View full text Add to dashboard Cite

show abstract

“…Then the following two BMO-seminorms are equivalent: The integral one While relations between Carleson measures and certain extensions of functions have been extended to spaces of homogeneous type (see e.g. [12,18,9]), these extensions are usually of a potential type (with conditions on kernel decay). The main drawback is that these extensions in general do not satisfy an equation such as (1.1).…”

mentioning

confidence: 99%

On BMO and Carleson measures on Riemannian manifolds

Brazke,

Schikorra,

Sire

2019

Preprint

View full text Add to dashboard Cite

Let M be a Riemannian n-manifold with a metric such that the manifold is Ahlfors-regular. We also assume either non-negative Ricci curvature, or that the Ricci curvature is bounded from below together with a bound on the gradient of the heat kernel. We characterize BMO-functions u : M → R by a Carleson measure condition of their σ-harmonic extension U : M × (0, ∞) → R. We make crucial use of a T (b) theorem proved by Hofmann, Mitrea, Mitrea, and Morris.As an application we show that the famous theorem of Coifman-Lions-Meyer-Semmes holds in this class of manifolds: Jacobians of W 1,n -maps from M to R n can be estimated against BMOfunctions, which now follows from the arguments for commutators recently proposed by Lenzmann and the second-named author using only harmonic extensions, integration by parts, and trace space characterizations.

show abstract

John–Nirenberg Type Inequalities for Musielak–Orlicz Campanato Spaces on Spaces of Homogeneous Type

Huy

2019

Vietnam J. Math.

View full text Add to dashboard Cite

Weighted BMO Type Spaces Associated to Admissible Functions and Applications

Cited by 7 publications

References 11 publications

John–Nirenberg Inequalities and Weight Invariant BMO Spaces

John–Nirenberg Inequalities and Weight Invariant BMO Spaces

On BMO and Carleson measures on Riemannian manifolds

John–Nirenberg Type Inequalities for Musielak–Orlicz Campanato Spaces on Spaces of Homogeneous Type

Contact Info

Product

Resources

About