Musielak–Orlicz Besov-type and Triebel–Lizorkin-type spaces

Yang, Dachun; Yuan, Wen; Zhuo, Ciqiang

doi:10.1007/s13163-013-0120-8

Cited by 41 publications

(25 citation statements)

References 53 publications

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“…Observe that [95, Theorem 3.1] characterizes Musielak-Orlicz Triebel-Lizorkin-type spaces by means of the Peetre maximal operator given below. Our atomic decompsoition results, Theorems 4.4 and 4.5 correspond to [95,Theorem 5.1]. By using the idea of [95, Theorem 6.9] or [50], we can prove the pseudo-differential operators with symbol in S 0 is bounded in A s M ϕ q ,r (R n ).…”

Section: 2mentioning

confidence: 67%

“…and the reverse Hölder condition In this sense, the results for E s M ϕ s ,r (R n ) can be covered by [95]. For example, Proposition 3.2 can be understood as the inhomogeneous version of [95,Proposition 2.19]. Observe that [95, Theorem 3.1] characterizes Musielak-Orlicz Triebel-Lizorkin-type spaces by means of the Peetre maximal operator given below.…”

Section: 2mentioning

confidence: 99%

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Generalized Morrey spaces and trace operator

2015

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Abstract. The theory of generalized Besov-Morrey spaces and generalized Triebel-LizorkinMorrey spaces is developed. Generalized Morrey spaces, which T. Mizuhara and E. Nakai proposed, are equipped with a parameter and a function. The trace property is one of the main focuses of the present paper, which will clarify the role of the parameter of generalized Morrey spaces. The quarkonial decomposition is obtained as an application of atomic decomposition. In the end, the relation between the function spaces dealt in the present paper and the foregoing researches is discussed.

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Section: 2mentioning

confidence: 67%

Section: 2mentioning

confidence: 99%

Generalized Morrey spaces and trace operator

2015

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“…Under the assumptions that 0 < p − ≤ p + ≤ 1 and p(·) satisfies the so-called globally log-Hölder continuous condition, which is denoted by p(·) ∈ C log (R n ) (see, for example, [86,88,89,90] for the details), the real-variable characterizations of H p(·) L (R n ) or its local version h p(·) L (R n ), including atoms, Lusin area functions, non-tangential and radial maximal functions associated with L, were established in [1,88,89,90]. It is worth pointing out that a general Musielak-Orlicz function ϕ as in Definition 1.4 may not have the form as in (1.12) (see, for example, [56,79,81]).…”

Section: Moreover the Variable Exponent Hardy Space Hmentioning

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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“…Recently, results from variable exponent spaces have been derived in the more general Musielak-Orlicz setting, see, e.g., [14,28,39,43]. Yang, Yuan and Zhou [54] considered versions of Besov and Triebel-Lizorkin spaces in this setting.…”

Section: Introductionmentioning

confidence: 99%