Generalized Morrey spaces and trace operator

Nakamura, Shohei; Noi, Takahiro; Sawano, Yoshihiro

doi:10.1007/s11425-015-5096-z

Cited by 55 publications

(63 citation statements)

References 79 publications

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“…Remark The space

{scriptA}_{{scriptM}_{q}^{ϕ}, r}^{s} false(R^{n} false)

does not depend on the different choices of admissible θ and τ ([, Theorem 1.4]).…”

Section: Function Spacesmentioning

confidence: 99%

“…The first reason is that the spaces

{scriptA}_{{scriptM}_{q}^{ϕ}, r}^{s} false(R^{n} false)

recover many spaces as well as the cases of Besov–Morrey spaces and Triebel–Lizorkin–Morrey spaces. In the following theorem, we introduce the result obtained by Nakamura, Noi and Sawano . We refer to [, Definition , Section 6.6] for the precise definitions of homogeneous generalized Triebel–Lizorkin–Morrey spaces

{\overset{E}{true}}_{{scriptM}_{q}^{ϕ}, r}^{s} false(R^{n} false)

and generalized Hardy–Morrey spaces

H {scriptM}_{q}^{ϕ} false(R^{n} false)

.…”

Section: Function Spacesmentioning

confidence: 99%

“…In the following theorem, we introduce the result obtained by Nakamura, Noi and Sawano . We refer to [, Definition , Section 6.6] for the precise definitions of homogeneous generalized Triebel–Lizorkin–Morrey spaces

{\overset{E}{true}}_{{scriptM}_{q}^{ϕ}, r}^{s} false(R^{n} false)

and generalized Hardy–Morrey spaces

H {scriptM}_{q}^{ϕ} false(R^{n} false)

. Theorem Let

0 < q < \infty

and let

ϕ \in {scriptG}_{q}

satisfy (2.5).…”

Section: Function Spacesmentioning

confidence: 99%

“…In this paper, we consider the generalized Besov–Morrey spaces

{scriptN}_{{scriptM}_{q}^{ϕ}, r}^{s} false(R^{n} false)

and the generalized Triebel–Lizorkin–Morrey spaces

{scriptE}_{{scriptM}_{q}^{ϕ}, r}^{s} false(R^{n} false)

introduced by Nakamura, Noi and Sawano . They have studied smooth atomic and quarkonical decompositions and the trace operator for these spaces.…”

Section: Introductionmentioning

confidence: 99%

“…The aim of this paper is twofold. The first aim is continuing to consider the theory of

{scriptA}_{{scriptM}_{q}^{ϕ}, r}^{s} false(R^{n} false)

due to . We consider a local mean characterization and a non‐smooth atomic decomposition.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Generalized Besov–Morrey spaces and generalized Triebel–Lizorkin–Morrey spaces on domains

Izuki

Noi

2019

Mathematische Nachrichten

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In this paper, we consider a non‐smooth atomic decomposition by using a smooth atomic decomposition. Applying the non‐smooth atomic decomposition, a local means characterization and a quarkonical decomposition, we obtain a pointwise multiplier and a trace operator for generalized Besov–Morrey spaces and generalized Triebel–Lizorkin–Morrey spaces on the whole space. We also develop the theory of those spaces on domains. We consider an extension operator and a trace operator on the upper half space and on compact oriented Riemannian manifolds.

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“…Remark The space

{scriptA}_{{scriptM}_{q}^{ϕ}, r}^{s} false(R^{n} false)

does not depend on the different choices of admissible θ and τ ([, Theorem 1.4]).…”

Section: Function Spacesmentioning

confidence: 99%

“…The first reason is that the spaces

{scriptA}_{{scriptM}_{q}^{ϕ}, r}^{s} false(R^{n} false)

{\overset{E}{true}}_{{scriptM}_{q}^{ϕ}, r}^{s} false(R^{n} false)

and generalized Hardy–Morrey spaces

H {scriptM}_{q}^{ϕ} false(R^{n} false)

.…”

Section: Function Spacesmentioning

confidence: 99%

{\overset{E}{true}}_{{scriptM}_{q}^{ϕ}, r}^{s} false(R^{n} false)

and generalized Hardy–Morrey spaces

H {scriptM}_{q}^{ϕ} false(R^{n} false)

. Theorem Let

0 < q < \infty

and let

ϕ \in {scriptG}_{q}

satisfy (2.5).…”

Section: Function Spacesmentioning

confidence: 99%

“…In this paper, we consider the generalized Besov–Morrey spaces

{scriptN}_{{scriptM}_{q}^{ϕ}, r}^{s} false(R^{n} false)

and the generalized Triebel–Lizorkin–Morrey spaces

{scriptE}_{{scriptM}_{q}^{ϕ}, r}^{s} false(R^{n} false)

introduced by Nakamura, Noi and Sawano . They have studied smooth atomic and quarkonical decompositions and the trace operator for these spaces.…”

Section: Introductionmentioning

confidence: 99%

“…The aim of this paper is twofold. The first aim is continuing to consider the theory of

{scriptA}_{{scriptM}_{q}^{ϕ}, r}^{s} false(R^{n} false)

due to . We consider a local mean characterization and a non‐smooth atomic decomposition.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Generalized Besov–Morrey spaces and generalized Triebel–Lizorkin–Morrey spaces on domains

Izuki

Noi

2019

Mathematische Nachrichten

Self Cite

View full text Add to dashboard Cite

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Generalized weighted Morrey spaces and classical operators

Nakamura

2016

Mathematische Nachrichten

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Hardy-Littlewood maximal operator, generalized fractional maximal operator, generalized fractional integral operator, singular integral operator MSC (2010) Primary: 42B25, Secondary: 42B35We introduce the notion of generalized weighted Morrey spaces and investigate the boundedness of some operators in these spaces, such as the Hardy-Littlewood maximal operator, generalized fractional maximal operators, generalized fractional integral operators, and singular integral operators. We also study their boundedness in the vector-valued setting.

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Regular wavelets and Triebel‐Lizorkin type oscillation spaces

Yang

Zhao

2017

Math Methods in App Sciences

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In this paper, we apply wavelets to study the Triebel-Lizorkin type oscillation spaceṡ  1 , 2 p,q (R n ) and identify them with the well-known Triebel-Lizorkin-Morrey spaces. Further, we prove that Calderón-Zygmund operators are bounded on 1 , 2 p,q (R n ). KEYWORDS Calderón-Zygmund operators, regular wavelets, Triebel-Lizorkin type oscillation spaceswhere the supremum is taken over all cubes Q and S 1 , 2 p,q,f denotes the set of all polynomials satisfying some special condition, see Definition 3.1 for the details. The wavelets are very useful in the research of function spaces and related topics. On the one hand, through wavelet characterization, we could understand the structure of the function spaces more thoroughly. On the other hand, many estimates associated with nonlinear term can be translated into the computation of wavelet coefficients. On the basis 6684

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Generalized Morrey spaces and trace operator

Cited by 55 publications

References 79 publications

Generalized Besov–Morrey spaces and generalized Triebel–Lizorkin–Morrey spaces on domains

Generalized Besov–Morrey spaces and generalized Triebel–Lizorkin–Morrey spaces on domains

Generalized weighted Morrey spaces and classical operators

Regular wavelets and Triebel‐Lizorkin type oscillation spaces

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