• 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}
}
• Published 2 March 2010
• Mathematics
• arXiv: Functional Analysis
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.
13 Citations
• Mathematics
• 2011
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
• Mathematics
The Journal of Geometric Analysis
• 2018
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
• Mathematics
The Journal of Geometric Analysis
• 2018
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
• Mathematics
• 2011
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
• Mathematics
Journal d'Analyse Mathématique
• 2012
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
• Mathematics
• 2014
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
• Mathematics
Journal of Pseudo-Differential Operators and Applications
• 2019
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
• Mathematics
Journal of Pseudo-Differential Operators and Applications
• 2019
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
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

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
• Mathematics
• 2006
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
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
We give John-Nirenberg type inequalities for the Morrey-Campanato spaces on .
• Mathematics
• 2005
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,
• Mathematics
• 2005
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
• Mathematics
• 2009
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,
• Mathematics
• 2006
$BMO$, 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