On the flows associated to selfadjoint operators on metric measure spaces

Bui, The Anh; D’Ancona, Piero; Duong, Xuan Thinh; Müller, Detlef

doi:10.1007/s00208-019-01857-w

Cited by 14 publications

(4 citation statements)

References 38 publications

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“…Fu et al [20] and Zhou et al [82] generalized the corresponding results in [32], respectively, to Musielak-Orlicz Hardy spaces and Hardy-Lorentz spaces. We refer the reader to [8,9,12,22,28,31,34,45,49,72] for more studies on the real-variable theory of function spaces over  and to [18,46,51,73] for their applications in the boundedness of operators; particularly, we refer the reader to [6,7,10] for some recent progress on the real-variable theory of function spaces on  associated with operators.…”

Section: Introductionmentioning

confidence: 99%

Hardy spaces associated with ball quasi‐Banach function spaces on spaces of homogeneous type: Characterizations of maximal functions, decompositions, and dual spaces

Yan

Yang

et al. 2023

Mathematische Nachrichten

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Let false(scriptX,ρ,μfalse)$({\mathcal {X}},\rho ,\mu )$ be a space of homogeneous type in the sense of Coifman and Weiss, and let Yfalse(scriptXfalse)$Y({\mathcal {X}})$ be a ball quasi‐Banach function space on X${\mathcal {X}}$, which supports both a Fefferman–Stein vector‐valued maximal inequality and the boundedness of the powered Hardy–Littlewood maximal operator on its associate space. The authors first introduce the Hardy space HY∗(X)$H_{Y}^*({\mathcal {X}})$, associated with Yfalse(scriptXfalse)$Y({\mathcal {X}})$, via the grand maximal function and then establish its various real‐variable characterizations, respectively, in terms of radial or nontangential maximal functions, atoms or finite atoms, and molecules. As an application, the authors give the dual space of HY∗(X)$H_{Y}^*({\mathcal {X}})$, which proves to be a ball Campanato‐type function space associated with Yfalse(scriptXfalse)$Y({\mathcal {X}})$. All these results have a wide range of generality and, particularly, even when they are applied to variable Hardy spaces, the obtained results are also new. The major novelties of this paper exist in that, to escape both the reverse doubling condition of μ and the triangle inequality of ρ, the authors cleverly construct admissible sequences of balls and fully use the geometrical properties of X${\mathcal {X}}$ expressed by dyadic reference points or dyadic cubes and, to overcome the difficulty caused by the lack of the good dense subset of HY∗(X)$H_{Y}^*({\mathcal {X}})$, the authors further prove that Yfalse(scriptXfalse)$Y({\mathcal {X}})$ can be embedded into the weighted Lebesgue space with certain special weight and then can fully use the known results of the weighted Lebesgue space.

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Section: Introductionmentioning

confidence: 99%

Hardy spaces associated with ball quasi‐Banach function spaces on spaces of homogeneous type: Characterizations of maximal functions, decompositions, and dual spaces

Yan

Yang

et al. 2023

Mathematische Nachrichten

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“…For more results on the Heisenberg group, see [7,8]. The case in the metric measure spaces is also considered, such as [4,13,14,15].…”

Section: Introductionmentioning

confidence: 99%

Decay estimates for a class of wave equations on the Heisenberg group

Song¹,

Yang²

2022

Preprint

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In this paper, we study a class of dispersive wave equations on the Heisenberg group H n . Based on the group Fourier transform on H n , the properties of the Laguerre functions and the stationary phase lemma, we establish the decay estimates for a class of dispersive semigroup on H n given by e itφ(L ) , where φ : R + → R is smooth, and L is the sub-Laplacian on H n . Finally, using the duality arguments, we apply the obtained results to derive the Strichartz inequalities for the solutions of some specific equations, such as the fractional Schrödinger equation, the fractional wave equation and the fourth-order Schrödinger equation.

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“…Fu et al [19] and Zhou et al [77] generalized the corresponding results in [30], respectively, to Musielak-Orlicz Hardy spaces and Hardy-Lorentz spaces. We refer the reader to [9,10,12,21,27,32,33,44,67] for more studies on the real-variable theory of function spaces over X, and [17,45,48,66] for their applications in the boundedness of operators; particularly, we refer the reader to [6,7,8] for some recent progress on the real-variable theory of function spaces on X associated with operators.…”

Section: Introductionmentioning

confidence: 99%

Hardy Spaces Associated with Ball Quasi-Banach Function Spaces on Spaces of Homogeneous Type: Characterizations of Maximal Functions, Decompositions, and Dual Spaces

Yan¹,

He²,

Yang³

et al. 2021

Preprint

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Let (X, ρ, µ) be a space of homogeneous type in the sense of Coifman and Weiss, and Y(X) a ball quasi-Banach function space on X, which supports a Fefferman-Stein vectorvalued maximal inequality, and the boundedness of the powered Hardy-Littlewood maximal operator on its associate space. The authors first introduce the Hardy space H * Y (X), associated with Y(X), via the grand maximal function, and then establish its various real-variable characterizations, respectively, in terms of radial or non-tangential maximal functions, atoms or finite atoms, and molecules. As an application, the authors give the dual space of H * Y (X), which proves to be a ball Campanato-type function space associated with Y(X). All these results have a wide range of generality and, particularly, even when they are applied to variable Hardy spaces, the obtained results are also new. The major novelties of this article exist in that, to escape the reverse doubling condition of µ and the triangle inequality of ρ, the authors cleverly construct admissible sequences of balls, and fully use the geometrical properties of X expressed by dyadic reference points or dyadic cubes and, to overcome the difficulty caused by the lack of the good dense subset of H * Y (X), the authors further prove that Y(X) can be embedded into the weighted Lebesgue space with certain special weight, and then can fully use the known results of the weighted Lebesgue space.

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On the flows associated to selfadjoint operators on metric measure spaces

Cited by 14 publications

References 38 publications

Hardy spaces associated with ball quasi‐Banach function spaces on spaces of homogeneous type: Characterizations of maximal functions, decompositions, and dual spaces

Hardy spaces associated with ball quasi‐Banach function spaces on spaces of homogeneous type: Characterizations of maximal functions, decompositions, and dual spaces

Decay estimates for a class of wave equations on the Heisenberg group

Hardy Spaces Associated with Ball Quasi-Banach Function Spaces on Spaces of Homogeneous Type: Characterizations of Maximal Functions, Decompositions, and Dual Spaces

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