Real-variable characterizations of Musielak-Orlicz-Hardy spaces associated with Schrödinger operators on domains

Chang, Der–Chen; Fu, Zunwei; Yang, Dachun; Yang, Sibei

doi:10.1002/mma.3501

Cited by 21 publications

(7 citation statements)

References 55 publications

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“…Moreover, when ϕ is as in (1.8), the Orlicz-Hardy spaces H Φ, r (Ω) and H Φ, z (Ω) and the weighted local Orlicz-Hardy spaces h Φ ω, r (Ω) and h Φ ω, z (Ω) were studied in [17,82,83]. Furthermore, the "geometric" Musielak-Orlicz-Hardy space H ϕ, L, r (Ω) on strongly Lipschitz domains associated with the Schrödinger operator was studied in [20].…”

Section: Applications To Musielak-orlicz-hardy Spaces On Lipschitz Do...mentioning

confidence: 99%

Atomic and maximal function characterizations of Musielak–Orlicz–Hardy spaces associated to non-negative self-adjoint operators on spaces of homogeneous type

Yang

2019

Collect. Math.

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Let X be a metric space with doubling measure and L a non-negative self-adjoint operator on L 2 (X) whose heat kernels satisfy the Gaussian upper bound estimates. Assume that the growth function ϕ : X×[0, ∞) → [0, ∞) satisfies that ϕ(x, ·) is an Orlicz function and ϕ(·, t) ∈ A ∞ (X) (the class of uniformly Muckenhoupt weights). Let H ϕ, L (X) be the Musielak-Orlicz-Hardy space defined via the Lusin area function associated with the heat semigroup of L. In this article, the authors characterize the space H ϕ, L (X) by means of atoms, non-tangential and radial maximal functions associated with L. In particular, when µ(X) < ∞, the local non-tangential and radial maximal function characterizations of H ϕ, L (X) are obtained. As applications, the authors obtain various maximal function and the atomic characterizations of the "geometric" Musielak-Orlicz-Hardy spaces H ϕ, r (Ω) and H ϕ, z (Ω) on the strongly Lipschitz domain Ω in R n associated with second-order self-adjoint elliptic operators with the Dirichlet and the Neumann boundary conditions; even when ϕ(x, t) := t for any x ∈ R n and t ∈ [0, ∞), the equivalent characterizations of H ϕ, z (Ω) given in this article improve the known results via removing the assumption that Ω is unbounded.(1.2)V(x, λr) ≤ Cλ n V (x, r) 2010 Mathematics Subject Classification. Primary 42B25; Secondary 42B35, 46E30, 30L99. Key words and phrases. Musielak-Orlicz-Hardy space, atom, maximal function, non-negative self-adjoint operator, Gaussian upper bound estimate, space of homogeneous type, strongly Lipschitz domain.

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Section: Applications To Musielak-orlicz-hardy Spaces On Lipschitz Do...mentioning

confidence: 99%

Atomic and maximal function characterizations of Musielak–Orlicz–Hardy spaces associated to non-negative self-adjoint operators on spaces of homogeneous type

Yang

2019

Collect. Math.

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“…where 0 < α ≤ 1, 1 < β ≤ 2. In the past twenty years, there has been a growing interest in the profit derived from advancing space theories [18][19][20], regular theories [21][22][23][24][25], operator methods [26][27][28][29][30], iterative techniques [31][32][33], the moving sphere method [34], critical point theories [35][36][37][38], and tempered fractional calculus. This surge in attention has not only propelled the rapid progress of these disciplines, but has also spurred corresponding contributions across various fields.…”

Section: Introductionmentioning

confidence: 99%

A Singular Tempered Sub-Diffusion Fractional Model Involving a Non-Symmetrically Quasi-Homogeneous Operator

Zhang,

Chen,

et al. 2024

Symmetry

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In this paper, we focus on the existence of positive solutions for a singular tempered sub-diffusion fractional model involving a quasi-homogeneous nonlinear operator. By using the spectrum theory and computing the fixed point index, some new sufficient conditions for the existence of positive solutions are derived. It is worth pointing out that the nonlinearity of the equation contains a tempered fractional sub-diffusion term, and is allowed to possess strong singularities in time and space variables. In particular, the quasi-homogeneous operator is a nonlinear and non-symmetrical operator.

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“…Due to the widespread application of differential equations in practice, in recent decades, many theories and methods of nonlinear analysis, such as the spaces theories [26][27][28][29][30][31], smoothness theories [32][33][34][35], operator theories [36][37][38], fixed-point theorems [18,21,24,25,[39][40][41], subsuper solution methods [17,[42][43][44][45], monotone iterative techniques [12,[46][47][48][49][50][51][52][53] and the variational method [54][55][56][57][58], have been developed to study various differential equations. For example, by adopting the fixed point theorem of the mixed monotone operator, Zhou et.…”

Section: Introductionmentioning

confidence: 99%

Upper and Lower Solution Method for a Singular Tempered Fractional Equation with a p-Laplacian Operator

et al. 2023

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In this paper, we consider the existence of positive solutions for a singular tempered fractional equation with a p-Laplacian operator. By constructing a pair of suitable upper and lower solutions of the problem, some new results on the existence of positive solutions for the equation including singular and nonsingular cases are established. The asymptotic behavior of the solution is also derived, which falls in between two known curves. The interesting points of this paper are that the nonlinearity of the equation may be singular in time and space variables and the corresponding operator can have a singular kernel.

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Real-variable characterizations of Musielak-Orlicz-Hardy spaces associated with Schrödinger operators on domains

Cited by 21 publications

References 55 publications

Atomic and maximal function characterizations of Musielak–Orlicz–Hardy spaces associated to non-negative self-adjoint operators on spaces of homogeneous type

Atomic and maximal function characterizations of Musielak–Orlicz–Hardy spaces associated to non-negative self-adjoint operators on spaces of homogeneous type

A Singular Tempered Sub-Diffusion Fractional Model Involving a Non-Symmetrically Quasi-Homogeneous Operator

Upper and Lower Solution Method for a Singular Tempered Fractional Equation with a p-Laplacian Operator

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