Applications of Littlewood-Paley Theory for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mover accent="true"><mml:mi>B</mml:mi><mml:mo>˙</mml:mo></mml:mover><mml:mi>σ</mml:mi></mml:msub></mml:mrow></mml:math>-Morrey Spaces to the Boundedness of Integral Operators

Komori-Furuya, Yasuo; Matsuoka, Katsuo; Nakai, Eiichi; Sawano, Yoshihiro

doi:10.1155/2013/859402

Cited by 11 publications

(4 citation statements)

References 33 publications

(37 reference statements)

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“…(iv) The Ḃσ -Morrey spaces Ḃσ (L p,λ ) studied by Y. Komori-Furuya et al [15], are contained in our definition as special cases, that is,…”

Section: Definitionsmentioning

confidence: 98%

2-microlocal spaces associated with Besov type and Triebel–Lizorkin type spaces

Saka

2021

Rev Mat Complut

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In this paper we introduce and investigate new 2-microlocal spaces associated with Besov type and Triebel-Lizorkin type spaces. We establish characterizations of these function spaces via the ϕ-transform, the atomic and molecular decomposition and the wavelet decomposition. As applications we consider boundedness of the Calderón-Zygmund operator and the pseudo-differential operator on the function spaces.

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“…(iv) The Ḃσ -Morrey spaces Ḃσ (L p,λ ) studied by Y. Komori-Furuya et al [15], are contained in our definition as special cases, that is,…”

Section: Definitionsmentioning

confidence: 98%

2-microlocal spaces associated with Besov type and Triebel–Lizorkin type spaces

Saka

2021

Rev Mat Complut

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“…The Ḃ𝜎 -Morrey spaces Ḃ𝜎 (𝐿 𝑝,𝜆 ) studied by Y. Komori-Furuya et al [16], are contained in our definition as special cases, that is, Ḃ𝜎 (𝐿 𝑝,𝜆 ) = 𝐴…”

Section: Definitionsmentioning

confidence: 99%

Local theory for 2‐microlocal Besov and Triebel–Lizorkin spaces of Jaffard type

Saka

2023

Mathematische Nachrichten

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“…Sawano, W. Sickel, and T. Tararykova (see previous studies [1][2][3][4][5] ). The results can be applied in the theory of generalized Bessel and Riesz potentials.…”

Section: Introductionmentioning

confidence: 99%

“…The first steps of generalization (for local Morrey spaces): introduction of a new parameter

q \in false(0, \infty false]

and considering a more general function

w false(t false) > 0

instead of

t^{- λ}

, so that

L M_{p q}^{w false(\cdot false)} = ({}, f \in L_{0} : false| false| f false| {false|}_{L M_{p q}^{w false(\cdot false)}} = {((), \int_{0}^{\infty} {([], w false(t false) false| false| f false| {false|}_{L_{p} false(B_{t} false)})}^{q} \frac{d t}{t})}^{\frac{1}{q}} < \infty),

with usual understanding for

q = \infty

. Some ways of generalization may be found in papers by V. Burenkov, A. Gogatishvili, V. Guliev, P. Jain, Y. Komori‐Furuya, K. Matsuoka, R. Mustafayev, T. Mizuhara, E. Nakai, E. Nursultanov, R. Oinarov, Y. Sawano, W. Sickel, and T. Tararykova (see previous studies 1—5 ). The results can be applied in the theory of generalized Bessel and Riesz potentials 6—8 …”

Section: Introductionmentioning

confidence: 99%