Hardy and Lipschitz spaces on subsets of $R^{n}$

Jonsson, Alf; Sjögren, Peter; Wallin, Hans

doi:10.4064/sm-80-2-141-166

Cited by 73 publications

(79 citation statements)

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“…There is quite an extensive literature concerning definitions of the Hardy spaces in a domain Ω ⊂ R n , [9,8,14,15,35,42,43,45]. Let us briefly outline the general concept of a maximal function of a distribution f ∈ D (Ω).…”

Section: Variants On Domains In R Nmentioning

confidence: 99%

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On the Product of Functions in BMO and H^\text{1}

Bonami¹,

Iwaniec²,

Jones³

et al. 2007

Ann. inst. Fourier

110

124

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Section: Variants On Domains In R Nmentioning

confidence: 99%

“…for Ω a bounded Lipschitz domain, and make some remarks on the definition of H 1 (Ω), which may be of independent interest, based on the developments in [8,15,42,43,45,54].…”

Section: In Either Case the Point-wise Product B · H Is Locally Integmentioning

confidence: 99%

On the Product of Functions in BMO and H^\text{1}

Bonami¹,

Iwaniec²,

Jones³

et al. 2007

Ann. inst. Fourier

110

124

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“…Une autre façon d'obtenir une décomposition en atomes dont le support est un cube inclus dans Ω, utilisée dans [77], est de procéder par dualité en utilisant un théorème de Jones sur les domaines ayant la propriété d'extension pour BM O (nous reviendrons sur ce point plus bas). Il estégalement possible d'utiliser les résultats de [216].…”

Section: Racines Carrées D'opérateurs Elliptiques Et Espaces De Hardy 37unclassified

Racines Carrées d'OPÉRATEURS Elliptiques Et Espaces De Hardy

Russ

2011

Confluentes Math.

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“…For more information on fractional order Sobolev spaces we refer the reader to [1,11,14,15,17,23] and the references contained therein.…”

Section: 1mentioning

confidence: 99%

On some degenerate non-local parabolic equation associated with the fractional $p$-Laplacian

Gal

Warma

2017

Dynamics of Partial Differential Equations

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Abstract. Let Ω ⊂ R N be an arbitrary bounded open set. We consider a degenerate parabolic equation associated to the fractional p-Laplace operator (−∆) s p (p ≥ 2, s ∈ (0, 1)) with the Dirichlet boundary condition and a monotone perturbation growing like |τ | q−2 τ, q > p and with bad sign at infinity as |τ | → ∞. We show the existence of locally-defined strong solutions to the problem with any initial condition u 0 ∈ L r (Ω) where r ≥ 2 satisfies r > N (q − p)/sp. Then, we prove that finite time blow-up is possible for these problems in the range of parameters provided for r, p, q and the initial datum u 0 . Contents

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Hardy and Lipschitz spaces on subsets of $R^{n}$

Cited by 73 publications

References 0 publications

On the Product of Functions in BMO and H^\text{1}

On the Product of Functions in BMO and H^\text{1}

Racines Carrées d'OPÉRATEURS Elliptiques Et Espaces De Hardy

On some degenerate non-local parabolic equation associated with the fractional $p$-Laplacian

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