リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

リケラボ 全国の大学リポジトリにある学位論文・教授論文を一括検索するならリケラボ論文検索大学・研究所にある論文を検索できる

大学・研究所にある論文を検索できる 「CHARACTERIZATION OF SOME FUNCTION SPACES BY SQUARE FUNCTIONS (Theory of function spaces and related topics)」の論文概要。リケラボ論文検索は、全国の大学リポジトリにある学位論文・教授論文を一括検索できる論文検索サービスです。

コピーが完了しました

URLをコピーしました

論文の公開元へ論文の公開元へ
書き出し

CHARACTERIZATION OF SOME FUNCTION SPACES BY SQUARE FUNCTIONS (Theory of function spaces and related topics)

SATO, SHUICHI 京都大学

2023.05

概要

This is a survey paper. I would like to state some recent results
in harmonic analysis related to characterization of function spaces by
square functions. The results include the following.
(1) Characterization of LP spaces, 1 < p < oo, by Littlewood-Paley
functions;
(2) Characterization of Sobolev spaces by Littlewood-Paley functions;
(3) Characterization of H 1 Sobolev spaces by square functions of
Lusin area integral type;
(4) Characterization of Hardy spaces HP on homogeneous groups
by Littlewood-Paley functions, where O < p :::; 1.
2. ...

この論文で使われている画像

参考文献

[1] R. Alabern, J. Mateu and J. Verdera, A new characterization of Sobolev spaces

on !Rn, Math. Ann. 354 (2012), 589- 626.

[2] A. Benedek, A. P. Calderon and R. Panzone, Convolution operators on Banach

space valued functions, Proc. Nat. Acad. Sci. U. S. A. 48 (1962) , 356- 365.

[3] A. P. Calderon and A. Torchinsky, Parabolic maximal functions associated with

a distribution, Advances in Math. 16 (1975) , 1-64.

[4] A. P. Calderon and A. Torchinsky, Parabolic maximal functions associated with

a distribution. II, Advances in Math. 24 (1977), 101-171.

[5] A. P. Calderon and A. Zygmund, Algebras of certain singular operators, Amer.

J. Math. 78 (1956) , 310- 320.

[6] F. Dai, J. Liu, D. Yang and W. Yuan, Littlewood-Paley characterizations of

fractional Sobolev spaces via averages on balls, arXiv: 1511.07598.

[7] Y. Ding and S. Sato, Singular integrals on product homogeneous groups, Integr.

Equ. Oper. Theory 76 (2013), 55-79.

[8] Y. Ding and S. Sato, Maximal singular integrals on product homogeneous

groups, Studia Math. 222 (2014), 41- 49.

[9] Y. Ding and S. Sato, Littlewood-Paley functions on homogeneous groups, Forum Math. 28 (2016) , 43- 55.

[10] C. Fefferman, Inequalities for strongly singular convolution operators, Acta

Math. 124 (1970), 9- 36.

193

[11] C. Fefferrnan and E. M. Stein, HP spaces of several variables, Acta Math. 129

(1972), 137- 193.

[12] G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups, Princeton Univ. Press, Princeton, N.J. 1982.

[13] J. Garcia-Cuerva and J.L. Rubio de Francia, Weighted Norm Inequalities and

Related Topics, North-Holland, Arnsterdarn, New York, Oxford, 1985.

[14] P. Hajlasz and Z. Liu, A Marcinkiewicz integral type characterization of the

Sobolev space, Publ. Mat. 61 (2017), 83- 104.

[15] L. Hormander, Estimates for translation invariant operators in LP spaces, Acta

Math. 104 (1960), 93- 139.

[16] M. Kaneko and G. Sunouchi, On the Littlewood-Paley and Marcinkiewicz functions in higher dimensions, Tohoku Math. J. 37 (1985), 343- 365.

[17] J. Marcinkiewicz, Sur quelues integrales de type de Dini, Annales de la Societe

Polonaise 17 (1938) , 42- 50.

[18] B. Muckenhoupt and R . L. Wheeden, Norm inequalities for the LittlewoodPaley function g";.., Trans . Arner. Math. Soc. 191 (1974), 95- 111.

[19] A. Nagel and E. M. Stein, Lectures on Pseudo-Differential Operators, Mathematical Notes 24, Princeton University Press, Princeton, NJ, 1979.

[20] J. Peetre, On spaces of Triebel-Lizorkin type, Ark. Mat. 13 (1975), 123- 130.

[21] S. Sato, Remarks on square functions in the Littlewood-Paley theory, Bull.

Austral. Math. Soc. 58 (1998), 199- 211.

[22] S. Sato, Multiparameter Marcinkiewicz integrals and a resonance theorem, Bull. Fae. Ed. Kanazawa Univ. Natur. Sci. 48 (1999), 1- 21.

(http ://hdl.handle.net/2297 /25017)

[23] S. Sato, Nonisotropic dilations and the method of rotations with weight, Proc.

Arner. Math. Soc. 140 (2012), 2791- 2801.

[24] S. Sato, Estimates for singular integrals on homogeneous groups, .J. Math.

Anal. Appl. 400 (2013), 311- 330.

[25] S. Sato, Boundedness of Littlewood-Paley operators, RIMS Kokyuroku

Bessatsu 49 (2014), 75- 101, Research Institute for Mathematical Sciences,

Kyoto University.

[26] S. Sato, Littlewood-Paley operators and Sobolev spaces, Illinois J. Math. 58

(2014), 1025- 1039.

[27] S. Sato, Weighted weak type (1,1) estimates for singular integrals with nonisotropic homogeneity, Ark. Mat. 54 (2016) , 157- 180.

[28] S. Sato, Square functions related to integral of Marcinkiewicz and Sobolev

spaces, Linear and onlinear Analysis 2(2) (2016) , Special Issue on ISBFS2015,

237- 252.

[29] S. Sato, Littlewood-Paley equivalence and homogeneous Fourier multipliers,

Integr. Equ. Oper. Theory 87 (2017), 15- 44.

[30] S. Sato, Spherical square functions of Marcinkiewicz type with Riesz potentials,

Arch. Math. 108( 4) (2017), 415- 426.

[31] S. Sato, Vector valued inequalities and Littlewood-Paley operators on Hardy

spaces, Hokkaido Math. J. 48 (2019), 61- 84, arXiv:1608.08059v2 [math.CA].

[32] S. Sato, Characterization of parabolic Hardy spaces by Littlewood-Paley functions, Results Math 73 (2018), 106. https://doi.org/10.1007 /s00025-018-08679, arXiv:1607.03645v2 [math.CA].

194

[33] S. Sato, Characterization of H 1 Sobolev spaces by square functions

of Marcinkiewicz type, J Fourier Anal Appl 25 (2019), 842- 873,

https://doi.org/10.1007 /s00041-018-9618-2.

[34] S. Sato, Bonndedness of Littlewood-Paley operators relative to non-isotropic

dilations, Czech Math. J. 69 (2019) , 337-351.

[35] S. Sato, Weak type estimates for functions of Marcinkiewicz type with fractional

integrals of mixed homogeneity, Math. Scand. 125(1) (2019), 135- 162.

[36] S. Sato, Hardy spaces on homogeneous groups and Littlewood-Paley

functions, Quart. J. Math. Published:25 January 2020, haz049, 1- 26,

https://doi.org/10.1093/qmath/haz049, Oxford University Press.

[37] S. Sato, F. Wang, D. Yang and W. Yuan, Generalized Littlewood-Paley characterizations of fractional Sobolev spaces, Communications in Contemporary

Mathematics 20(7) (2018), 1750077 (48 pages).

[38] E. M. Stein, The characterization of functions arising as potentials, Bull. Amer.

Math. Soc. 67 (1961) , 102- 104.

[39] E. M. Stein, Singular Integrals and Differentiability Properties of Functions,

Princeton Univ. Press, 1970.

[40] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean

Spaces, Princeton Univ. Press, 1971.

[41] J. -0. Stromberg and A. Torchinsky, Weighted Hardy Spaces, Lecture Notes in

Math. 1381, Springer-Verlag, Berlin Heidelberg New York London Paris Tokyo

Hong Kong, 1989.

[42] T. Tao, The weak-type (1, 1) of LlogL homogeneous convolution operator, Indiana Univ. Math . .T. 48 (1999) , 1547- 1584.

[43] A. Uchiyama, Characterization of HP(JR.n) in terms of generalized LittlewoodPaley g-functions, Studia Math. 81 (1985), 135- 158.

[44] D. Waterman, On an integral of Marcinkiewicz, Trans. Amer. Math. Soc. 91

(1959), 129- 138.

[45] A. Zygmund, On certain integrals, Trans. Amer. Math. Soc. 58 (1944), 170204.

DEPARTMENT OF MATHEMATICS, FACULTY OF EDUCATION, KANAZAWA UNIVERSITY, KANAZAWA 920-1192, JAPAN

E-mail address: shui chi ©kenroku. kanazawa -u. ac . j p

...

参考文献をもっと見る

全国の大学の
卒論・修論・学位論文

一発検索!

この論文の関連論文を見る