Weak Herz-type Hardy spaces with variable exponents and applications
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Let $\alpha\in(0,\infty)$, $p\in(0,\infty)$ and $q(\cdot): {\R}^{n}\rightarrow[1,\infty)$ satisfy the globally log-H\"{o}lder continuity condition. We introduce the weak Herz-type Hardy spaces with variable exponents via the radial grand maximal operator and to give its maximal characterizations, we establish a version of the boundedness of the Hardy-Littlewood maximal operator $M$ and the Fefferman-Stein vector-valued inequality on the weak Herz spaces with variable exponents. We also obtain the atomic and the molecular decompositions of the weak Herz-type Hardy spaces with variable exponents. As an application of the atomic decomposition we provide various equivalent characterizations of our spaces by means of the Lusin area function, the Littlewood-Paley $g$-function and the Littlewood-Paley $g^{\ast}_{\lambda}$-function.
Abstract
Let $\alpha\in(0,\infty)$, $p\in(0,\infty)$ and $q(\cdot): {\R}^{n}\rightarrow[1,\infty)$ satisfy the globally log-H\"{o}lder continuity condition. We introduce the weak Herz-type Hardy spaces with variable exponents via the radial grand maximal operator and to give its maximal characterizations, we establish a version of the boundedness of the Hardy-Littlewood maximal operator $M$ and the Fefferman-Stein vector-valued inequality on the weak Herz spaces with variable exponents. We also obtain the atomic and the molecular decompositions of the weak Herz-type Hardy spaces with variable exponents. As an application of the atomic decomposition we provide various equivalent characterizations of our spaces by means of the Lusin area function, the Littlewood-Paley $g$-function and the Littlewood-Paley $g^{\ast}_{\lambda}$-function.
참고문헌 (34)
- A. Almeida, "Atomic and molecular decompositions in variable exponent 2-microlocal spaces and applications", J. Funct. Anal, 270(5), pp.1888~1921 (2016)[DOI]
- T. Aoki, "Locally bounded linear topological spaces", Proc. Imp. Acad. Tokyo, 18, pp.588~594 (1942)
- A. -P. Calderon, "An atomic decomposition of distributions in parabolic Hp spaces", Adv. Math, 25(3), pp.216~225 (1977)[DOI]
- D. Cruz-Uribe, "The boundedness of classical operators on variable Lp spaces", Ann. Acad. Sci. Fenn. Math, 31(1), pp.239~264 (2006)
- "Ann. Acad. Sci. Fenn. Math", 2004, 247~249
- D. Cruz-Uribe, "Variable Hardy spaces", Indiana Univ. Math. J, 63(2), pp.447~493 (2014)[DOI]
- L. Diening, "Lecture Notes in Math. 2017" (2011), Springer
- L. Diening, "Function spaces of variable smoothness and integrability", J. Funct. Anal, 256(6), pp.1731~1768 (2009)[DOI]
- C. Fefferman, "Interpolation between Hp spaces: the real method", Trans. Amer. Math. Soc, 191, pp.75~81 (1974)[DOI]
- R. Fefferman, "The space WeakH1", Studia Math, 85(1), pp.1~16 (1986)[DOI]
- G. B. Folland, "Math. Notes, 28" (1982), Princeton University Press
- L. Grafakos, "Grad. Texts in Math. 250" (2014), Springer
- L. Grafakos, "Adv. Lect. Math. (ALM) 34", pp.177~202 (2016), Int. Press
- D. He, "Square function characterization of weak Hardy spaces", J. Fourier Anal. Appl, 20(5), pp.1083~1110 (2014)[DOI]
- S. Hou, "Lusin area function and molecular characterizations of Musielak-Orlicz Hardy spaces and their applications", Commun. Contemp. Math, 15(6), pp.37~ (2013)[DOI]
- M. Izuki, "Boundedness of sublinear operators on Herz spaces with variable exponent and application to wavelet characterization", Anal. Math, 36(1), pp.33~50 (2010)[DOI]
- M. Izuki, "Vector-valued inequalities on Herz spaces and characterizations of Herz-Sobolev spaces with variable exponent", Glas. Mat. Ser. III, 45(2), pp.475~503 (2010)[DOI]
- M. Izuki, "Function spaces with variable exponents-an intro-duction", Sci. Math. Jpn, 77(2), pp.187~315 (2014)
- M. Izuki, "Boundedness of fractional integrals on weighted Herz spaces with variable exponent", J. Inequal. Appl, 2016, pp.15~ (2016)[DOI]
- Y. Jiao, "Variable Hardy-Lorentz spaces Hp(·);q(Rn)", Math. Nachr, 292(2), pp.309~349 (2019)[DOI]
- O. Kovaack, "On spaces Lp(x) and Wk,p(x)", Czechoslovak Math. J, 41, pp.592~618 (1991)
- Y. Liang, "Weak Musielak-Orlicz Hardy spaces and applications", Math. Nachr, 289(5-6), pp.634~677 (2016)[DOI]
- S. Lu, "Herz Type Spaces and Their Applications" (2008), Science Press
- E. Nakai, "Hardy spaces with variable exponents and generalized Cam-panato spaces", J. Funct. Anal, 262(9), pp.3665~3748 (2012)[DOI]
- A. Nekvinda, "Hardy-Littlewood maximal operator on Lp(x)(R)", Math. Inequal. Appl, 7(2), pp.255~265 (2004)[DOI]
- S. Rolewicz, "On a certain class of linear metric spaces", Bull. Acad. Polon. Sci. Cl. III, 5, pp.471~473 (1957)
- K. Saibi, "Intrinsic square function characterizations of variable Hardy-Lorentz spaces", J. Funct. Spaces, 2020, pp.9~ (2020)[DOI]
- Y. Sawano, "Atomic decompositions of Hardy spaces with variable exponents and its application to bounded linear operators", Integral Equations Operator Theory, 77(1), pp.123~148 (2013)[DOI]
- E. M. Stein, "Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals", PMS, 43 (1993)
- M. H. Taibleson, "The molecular characterization of certain Hardy spaces, in Representation theorems for Hardy spaces", Asterisque, 77, pp.67~149 (1980)
- J. Xu, "Variable Besov and Triebel-Lizorkin spaces", Ann. Acad. Sci. Fenn. Math, 33(2), pp.511~522 (2008)
- X. Yan, "Variable weak Hardy spaces and their applications", J. Funct. Anal, 271(10), pp.2822~2887 (2016)[DOI]
- D. Yang, "Triebel-Lizorkin type spaces with variable exponents", Banach J. Math. Anal, 9(4), pp.146~202 (2015)[DOI]
- C. Zhuo, "Intrinsic square function characterizations of Hardy spaces with variable exponents", Bull. Malays. Math. Sci. Soc, 39(4), pp.1541~1577 (2016)[DOI]