Musielak-Orlicz Besov-Type and Triebel-Lizorkin-Type Spaces

Yang, Dachun; Liang, Yiyu; Ky, Luong Dang

doi:10.1007/978-3-319-54361-1_9

Cited by 3 publications

(3 citation statements)

References 35 publications

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“…For these reasons, concern about generalized Orlicz spaces has been also increasing, and we believe that most classical results in functional analysis can be obtained if we impose a suitable condition on the generating function ϕ(•). We refer to recent results [20,23,28,30,33,34,35,36,37,42,43,53] for the analysis of generalized Orlicz spaces. In particular, in [30,32] the authors have presented a natural and weaker condition on ϕ(•) which implies the conditions for the specific examples we mentioned above.…”

Section: Introductionmentioning

confidence: 99%

Calderón–Zygmund estimates in generalized Orlicz spaces

Hästö

2019

Journal of Differential Equations

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We establish the W 2,ϕ(•) -solvability of the linear elliptic equations in nondivergence form under a suitable, essentially minimal, condition of the generalized Orlicz function ϕ(•) = ϕ(x, t), by deriving Calderón-Zygmund type estimates. The class of generalized Orlicz spaces we consider here contains as special cases classical Lebesgue and Orlicz spaces, as well as non-standard growth cases like variable exponent and double phase growth.

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Section: Introductionmentioning

confidence: 99%

Calderón–Zygmund estimates in generalized Orlicz spaces

Hästö

2019

Journal of Differential Equations

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“…As well as interesting theoretical considerations, the motivation to study Musielak-Orlicz-type space comes from applications to elasticity, fluid dynamics, image processing, nonlinear partial differential equations and the calculus of variation (see, for example, [3,4]). More Musielak-Orlicz-type spaces are referred to in [5,19,[21][22][23][37][38][39]. We refer the reader to [38] for a complete survey of the real-variable theory of Musielak-Orlicz Hardy spaces.…”

Section: Introductionmentioning

confidence: 99%

Two boundedness criteria for a class of operators on Musielak–Orlicz Hardy spaces and applications

Qiu

Xiong

et al. 2019

Proceedings of the Edinburgh Mathematical Society

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Let φ : ℝn × [0, ∞) → [0, ∞) satisfy that φ(x, · ), for any given x ∈ ℝn, is an Orlicz function and φ( · , t) is a Muckenhoupt A∞ weight uniformly in t ∈ (0, ∞). The (weak) Musielak–Orlicz Hardy space Hφ(ℝn) (WHφ(ℝn)) generalizes both the weighted (weak) Hardy space and the (weak) Orlicz Hardy space and hence has wide generality. In this paper, two boundedness criteria for both linear operators and positive sublinear operators from Hφ(ℝn) to Hφ(ℝn) or from Hφ(ℝn) to WHφ(ℝn) are obtained. As applications, we establish the boundedness of Bochner–Riesz means from Hφ(ℝn) to Hφ(ℝn), or from Hφ(ℝn) to WHφ(ℝn) in the critical case. These results are new even when φ(x, t): = Φ(t) for all (x, t) ∈ ℝn × [0, ∞), where Φ is an Orlicz function.

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“…Recently, results from variable exponent spaces have been derived in the more general Musielak–Orlicz setting, see, e.g., . Yang, Yuan and Zhou considered versions of Besov and Triebel–Lizorkin spaces in this setting.…”

Section: Introductionmentioning

confidence: 99%