• Corpus ID: 14576968

Abstract framework for John Nirenberg inequalities and applications to Hardy spaces

@article{Bernicot2010AbstractFF,
  title={Abstract framework for John Nirenberg inequalities and applications to Hardy spaces},
  author={Fr{\'e}d{\'e}ric Bernicot and Jiman Zhao},
  journal={arXiv: Functional Analysis},
  year={2010}
}
In this paper, we develop an abstract framework for John-Nirenberg inequalities associated to BMO-type spaces. This work can be seen as the sequel of [5], where the authors introduced a very general framework for atomic and molecular Hardy spaces. Moreover, we show that our assumptions allow us to recover some already known John-Nirenberg inequalities. We give applications to the atomic Hardy spaces too. 
View PDF on arXiv
13 Citations
Background Citations
5
Methods Citations
2

13 Citations

Abstract Hardy spaces with variable exponents

Self-improving properties for abstract Poincaré type inequalities

We study self-improving properties in the scale of Lebesgue spaces of generalized Poincar e inequalities in the Euclidean space. We present an abstract setting where oscillations are given by certain…

John–Nirenberg Inequalities and Weight Invariant BMO Spaces

This work explores new deep connections between John–Nirenberg type inequalities and Muckenhoupt weight invariance for a large class of BMO-type spaces. The results are formulated in a very general…

John–Nirenberg Inequalities and Weight Invariant BMO Spaces

This work explores new deep connections between John–Nirenberg type inequalities and Muckenhoupt weight invariance for a large class of BMO-type spaces. The results are formulated in a very general…

Algebra properties for Sobolev spaces — applications to semilinear PDEs on manifolds

In this work, we aim to prove algebra properties for generalized Sobolev spaces Ws,p ∩ L∞ on a Riemannian manifold (or more general homogeneous type space as graphs), where Ws,p is of Bessel-type…

Algebra properties for Sobolev spaces — applications to semilinear PDEs on manifolds

In this work, we aim to prove algebra properties for generalized Sobolev spaces Ws,p ∩ L∞ on a Riemannian manifold (or more general homogeneous type space as graphs), where Ws,p is of Bessel-type…

Dispersive estimates with loss of derivatives via the heat semigroup and the wave operator

This paper aims to give a general (possibly compact or noncompact) analog of Strichartz inequalities with loss of derivatives, obtained by Burq, Gerard, and Tzvetkov [19] and Staffilani and Tataru…

Bilinear square spectral multipliers on stratified groups

In this paper, on stratified groups, we give a reasonable definition of bilinear square spectral multiplier and its commutator. Then we study their boundedness on weighted Lebesgue spaces under the…

Bilinear square spectral multipliers on stratified groups

In this paper, on stratified groups, we give a reasonable definition of bilinear square spectral multiplier and its commutator. Then we study their boundedness on weighted Lebesgue spaces under the…

Musielak–Orlicz Hardy Spaces Associated with Divergence Form Elliptic Operators Without Weight Assumptions

Abstract Let L be a divergence form elliptic operator with complex bounded measurable coefficients, let ω be a positive Musielak-Orlicz function on (0, ∞) of uniformly strictly critical lower-type pω…

References

SHOWING 1-10 OF 18 REFERENCES

New Abstract Hardy Spaces

Use of abstract Hardy spaces, real interpolation and applications to bilinear operators

This paper can be considered as the sequel of Bernicot and Zhao (J Func Anal 255:1761–1796, 2008), where the authors have proposed an abstract construction of Hardy spaces H1. They shew an…

Abstract Hardy-Sobolev spaces and interpolation

Hardy and BMO spaces associated to divergence form elliptic operators

Consider a second order divergence form elliptic operator L with complex bounded measurable coefficients. In general, operators based on L, such as the Riesz transform or square function, may lie…

Exponential self-improvement of generalized Poincaré inequalities associated with approximations of the identity and semigroups

The purpose of this paper is to present a general method that allows us to study exponential self-improving properties of generalized Poincaré inequalities associated with an approximation of the…

John-Nirenberg Type Inequalities for the Morrey-Campanato Spaces

We give John-Nirenberg type inequalities for the Morrey-Campanato spaces on .

Duality of Hardy and BMO spaces associated with operators with heat kernel bounds on product domains

Let L be the infinitesimal generator of an analytic semigroup on L2 (ℝ) with suitable upper bounds on its heat kernels, and L has a bounded holomorphic functional calculus on L2 (ℝ). In this article,…

A characterization of the Morrey-Campanato spaces

Abstract.In this paper, we give a new characterization of the Morrey–Campanato spaces by using the convolution φtB*f(x) to replace the minimizing polynomial PBf of a function f in the…

Remarks on spectral multiplier theorems on Hardy spaces associated with semigroups of operators

Let L be a non-negative, self-adjoint operator on L^2(\Omega), where (\Omega, d \mu) is a space of homogeneous type. Assume that the semigroup {T_t}_{t>0} generated by -L satisfies Gaussian bounds,…

FUNCTIONS OF BOUNDED MEAN OSCILLATION

$BMO$, the space of functions of bounded mean oscillation, was first introduced by F. John and L. Nirenberg in 1961. It became a focus of attention when C. Fefferman proved that $BMO$ is the dual of…