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Brézis-Gallouët-Wainger type inequality for Besov-Morrey spaces

100%
Sawano Y.
Studia Mathematica
|
2010
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tom 196
|
nr 1
91-101
EN
The aim of the present paper is to obtain an inequality of Brézis-Gallouët-Wainger type for Besov-Morrey spaces. We investigate these spaces in a self-contained manner. Also, we verify that our result is sharp.
2
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Non-smooth decomposition of homogeneous Triebel−Lizorkin−Morrey spaces

64%
Asami K., Sawano Y.
Commentationes Mathematicae
|
2018
|
tom 58
|
nr 1-2
EN
The aim of this paper is to develop a theory of non-smooth decomposition in Triebel−Lizorkin−Morrey spaces. As a byproduct, we obtain the non-smooth decomposition results for Hardy spaces and Morrey spaces. The result extends what Frazier and Jawerth obtained in 1990 with the parameters subject to a condition. Unlike this foregoing work, the result in this paper is valid for all admissible parameters for Triebel−Lizorkin−Morrey spaces. As an application, an improvement of the Olsen inequality is obtained.
3
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The John-Nirenberg type inequality for non-doubling measures

64%
Sawano Y., Tanaka H.
Studia Mathematica
|
2007
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tom 181
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nr 2
153-170
EN
X. Tolsa defined a space of BMO type for positive Radon measures satisfying some growth condition on $ℝ^{d}$. This new BMO space is very suitable for the Calderón-Zygmund theory with non-doubling measures. Especially, the John-Nirenberg type inequality can be recovered. In the present paper we introduce a localized and weighted version of this inequality and, as applications, we obtain some vector-valued inequalities and weighted inequalities for Morrey spaces.
4
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Weighted norm inequalities for multilinear fractional operators on Morrey spaces

51%
Iida T., Sato E., Sawano Y., Tanaka H.
Studia Mathematica
|
2011
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tom 205
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nr 2
139-170
EN
A weighted theory describing Morrey boundedness of fractional integral operators and fractional maximal operators is developed. A new class of weights adapted to Morrey spaces is proposed and a passage to the multilinear cases is covered.
5
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A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces

50%
Liang Y., Yang D., Yuan W., Sawano Y., Ullrich T.
Instytut Matematyczny Polskiej Akademii Nauk
EN
In this paper, the authors propose a new framework under which a theory of generalized Besov-type and Triebel-Lizorkin-type function spaces is developed. Many function spaces appearing in harmonic analysis fall under the scope of this new framework. The boundedness of the Hardy-Littlewood maximal operator or the related vector-valued maximal function on any of these function spaces is not required to construct these generalized scales of smoothness spaces. Instead, a key idea used is an application of the Peetre maximal function. This idea originates from recent findings in the abstract coorbit space theory obtained by Holger Rauhut and Tino Ullrich. In this new setting, the authors establish the boundedness of pseudo-differential operators based on atomic and molecular characterizations and also the boundedness of Fourier multipliers. Characterizations of these function spaces by means of differences and oscillations are also established. As further applications of this new framework, the authors reexamine and polish some existing results for many different scales of function spaces.
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