Hardy and BMO spaces associated to divergence form elliptic operators

Hofmann, Steve; Mayboroda, Svitlana

doi:10.1007/s00208-008-0295-3

Cited by 259 publications

(435 citation statements)

References 28 publications

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“…Nous procédons ainsi: on a par définition Dans [197], les auteurs définissent une molécule comme une fonction m ∈ L 2 (R n ) (l'exposant 2 pouvantêtre modifié dans un intervalle autour de 2) qui peut s'écrire [197] pour la définition exacte).…”

Section: Le Dual De Hunclassified

Racines Carrées d'OPÉRATEURS Elliptiques Et Espaces De Hardy

Russ

2011

Confluentes Math.

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Section: Le Dual De Hunclassified

Racines Carrées d'OPÉRATEURS Elliptiques Et Espaces De Hardy

Russ

2011

Confluentes Math.

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“…Using the L 2 off-diagonal decays of the semigroup (see Section 2.3 of [2]), it is quite "classical" to obtain the assumptions of our Proposition 4.7 (the arguments are very similar to those of Theorem 6.1 in [2] (step3) and those in [27] We have let the details to the interested reader. Here we want just explain how use the bilinear theory to study quadratic functionals.…”

Section: Applications To Quadratic Functionalsmentioning

confidence: 99%

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

Bernicot

2009

Math. Z.

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This paper can be considered as the sequel of [6], where the authors have proposed an abstract construction of Hardy spaces H 1 . They shew an interpolation result for these Hardy spaces with the Lebesgue spaces. Here we describe a more precise result using the real interpolation theory and we clarify the use of Hardy spaces. Then with the help of the bilinear interpolation theory, we then give applications to study bilinear operators on Lebesgue spaces. These ideas permit us to study singular operators with singularities similar to those of bilinear Calderón-Zygmund operators in a far more abstract framework as in the euclidean case.

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“…Yang and his cooperators discussed new Orlicz-Hardy spaces associated with operators [10][11][12][13]. For more results, we refer to [14][15][16][17][18][19] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Herz-Type Hardy Spaces Associated with Operators

Chai

Yan

Zhao

2018

Journal of Function Spaces

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Suppose is a nonnegative, self-adjoint differential operator. In this paper, we introduce the Herz-type Hardy spaces associated with operator . Then, similar to the atomic and molecular decompositions of classical Herz-type Hardy spaces and the Hardy space associated with operators, we prove the atomic and molecular decompositions of the Herz-type Hardy spaces associated with operator . As applications, the boundedness of some singular integral operators on Herz-type Hardy spaces associated with operators is obtained.

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Hardy and BMO spaces associated to divergence form elliptic operators

Cited by 259 publications

References 28 publications

Racines Carrées d'OPÉRATEURS Elliptiques Et Espaces De Hardy

Racines Carrées d'OPÉRATEURS Elliptiques Et Espaces De Hardy

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

Herz-Type Hardy Spaces Associated with Operators

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