Musielak–Orlicz Besov-type and Triebel–Lizorkin-type spaces
Tóm tắt
Từ khóa
Tài liệu tham khảo
Almeida, A., Hästö, P.: Besov spaces with variable smoothness and integrability. J. Funct. Anal. 258, 1628–1655 (2010)
Astala, K., Iwaniec, T., Koskela, P., Martin, G.: Mappings of BMO-bounded distortion. Math. Ann. 317, 703–726 (2000)
Birnbaum, Z., Orlicz, W.: Über die Verallgemeinerung des Begriffes der zueinander konjugierten Potenzen. Studia Math. 3, 1–67 (1931)
Bonami, A., Feuto, J., Grellier, S.: Endpoint for the DIV-CURL lemma in Hardy spaces. Publ. Mat. 54, 341–358 (2010)
Bonami, A., Grellier, S.: Hankel operators and weak factorization for Hardy–Orlicz spaces. Colloq. Math. 118, 107–132 (2010)
Bonami, A., Grellier, S., Ky, L.D.: Paraproducts and products of functions in BMO $$({\mathbb{R}})$$ and $$H^1(({\mathbb{R}}))$$ through wavelets. J. Math. Pure Appl. 97, 230–241 (2012)
Bonami, A., Iwaniec, T., Jones, P., Zinsmeister, M.: On the product of functions in BMO and $$H^1$$ . Ann. Inst. Fourier (Grenoble) 57, 1405–1439 (2007)
Bownik, M.: Atomic and molecular decompositions of anisotropic Besov spaces. Math. Z. 250, 539–571 (2005)
Bownik, M., Ho, K.-P.: Atomic and molecular decompositions of anisotropic Triebel–Lizorkin spaces. Trans. Am. Math. Soc. 358, 1469–1510 (2005)
Bownik, M.: Anisotropic Triebel–Lizorkin spaces with doubling measures. J. Geom. Anal. 17, 387–424 (2007)
Bownik, M., Li, B., Yang, D., Zhou, Y.: Weighted anisotropic Hardy spaces and their applications in boundedness of sublinear operators. Indiana Univ. Math. J. 57, 3065–3100 (2008)
Bui, H.Q.: Weighted Besov and Triebel spaces: interpolation by the real method. Hiroshima Math. J. 12, 581–605 (1982)
Bui, H.Q., Paluszyński, M., Taibleson, M.: A maximal function characterization of weighted Besov–Lipschitz and Triebel–Lizorkin spaces. Studia Math. 119, 219–246 (1996)
Bui, H.Q., Paluszyński, M., Taibleson, M.: Characterization of the Besov–Lipschitz and Triebel–Lizorkin spaces. The case $$q<1$$ . J. Fourier Anal. Appl. 3, 837–846 (1997)
Cho, Y.-K.: Continuous characterization of the Triebel–Lizorkin spaces and Fourier multipliers. Bull. Korean Math. Soc. 47, 839–857 (2010)
Cho, Y.-K., Kim, D.: A Fourier multiplier theorem on the Besov–Lipschitz spaces. Korean J. Math. 16, 85–90 (2008)
Dafni, G., Xiao, J.: Some new tent spaces and duality theorems for fractional Carleson measures and $$Q_\alpha ({\mathbb{R}}^n) $$ . J. Funct. Anal. 208, 377–422 (2004)
Diening, L., Hästö, P., Roudenko, S.: Function spaces of variable smoothness and integrability. J. Funct. Anal. 256, 1731–1768 (2009)
Diening, L., Harjulehto, P., Hästö, P., R $$\mathring{\rm u}$$ žička, M.: Lebesgue and Sobolev Spaces with Variable Exponents. Lecture Notes in Mathematics, 2017. Springer, Heidelberg (2011)
Essén, M., Janson, S., Peng, L.Z., Xiao, J.: $$Q$$ spaces of several real variables. Indiana Univ. Math. J. 49, 575–615 (2000)
Fan, M.: Lions–Peetre’s interpolation methods associated with quasi-power functions and some applications. Rocky Mt. J. Math. 36, 1487–1509 (2006)
Fernandez, D.L., Garcia, J.B.: Interpolation of Orlicz-valued function spaces and U.M.D. property. Studia Math. 99, 23–40 (1991)
Frazier, M., Jawerth, B.: A discrete transform and decompositions of distribution spaces. J. Funct. Anal. 93, 34–170 (1990)
Grafakos, L., Torres, R.H.: Pseudodifferential operators with homogeneous symbols. Mich. Math. J. 46, 261–269 (1999)
Hou, S., Yang, D., Yang, S.: Lusin area function and molecular characterizations of Musielak–Orlicz Hardy spaces and their applications. arXiv:1201.1945
Hou, S., Yang, D., Yang, S.: Musielak-Orlicz BMO-type spaces associated with generalized approximations to the identity. arXiv:1303.6366 (2013)
Iwaniec, T., Onninen, J.: $$H^1$$ -estimates of Jacobians by subdeterminants. Math. Ann. 324, 341–358 (2002)
Izuki, M., Sawano, Y.: Atomic decomposition for weighted Besov and Triebel–Lizorkin spaces. Math. Nachr. 285, 103–126 (2012)
Izuki, M., Sawano, Y., Tanaka, H.: Weighted Besov–Morrey spaces and Triebel–Lizorkin spaces. In: Harmonic Analysis and Nonlinear Partial Differential Equations, RIMS Kôkyûroku Bessatsu, B22, Research Institute for Mathematical Sciences (RIMS), Kyoto, pp. 21–60 (2010)
Kozono, H., Yamazaki, M.: Semilinear heat equations and the Navier–Stokes equation with distributions in new function spaces as initial data. Commun. Partial Differ. Equ. 19, 959–1014 (1994)
Ky, L.D.: New Hardy spaces of Musielak–Orlicz type and boundedness of sublinear operators. arXiv:1103.3757
Ky, L.D.: Bilinear decompositions and commutators of singular integral operators. Trans. Am. Math. Soc. 365, 2931–2958 (2013)
Liang, Y., Huang, J., Yang, D.: New real-variable characterizations of Musielak–Orlicz Hardy spaces. J. Math. Anal. Appl. 395, 413–428 (2012)
Liang, Y., Sawano, Y., Ullrich, T., Yang, D., Yuan, W.: New characterizations of Besov–Triebel–Lizorkin–Hausdorff spaces including coorbits and wavelets. J. Fourier Anal. Appl. 18, 1067–1111 (2012)
Martínez, S., Wolanski, N.: A minimum problem with free boundary in Orlicz spaces. Adv. Math. 218, 1914–1971 (2008)
Mazzucato, A.: Function space theory and applications to non-linear PDE. Trans. Am. Math. Soc. 355, 1297–1369 (2003)
Musielak, J.: Orlicz Spaces and Modular Spaces. Lecture Notes in Mathematics, vol. 1034, Springer, Berlin (1983)
Nakai, E., Yabuta, K.: Pointwise multipliers for functions of bounded mean oscillation. J. Math. Soc. Jpn. 37, 207–218 (1985)
Nakai, E., Sawano, Y.: Hardy spaces with variable exponents and generalized Campanato spaces. J. Funct. Anal. 262, 3665–3748 (2012)
Noi, T., Sawano, Y.: Complex interpolation of Besov spaces and Triebel–Lizorkin spaces with variable exponents. J. Math. Anal. Appl. 387, 676–690 (2012)
Orlicz, W.: Über eine gewisse Klasse von Räumen vom Typus B. Bull. Int. Acad. Pol. Ser. A 8, 207–220 (1932)
Pick, L., Sickel, W.: Several types of intermediate Besov–Orlicz spaces. Math. Nachr. 164, 141–165 (1993)
Rao, M.M., Ren, Z.D.: Theory of Orlicz Spaces. Monographs and Textbooks in Pure and Applied Mathematics, vol. 146, Marcel Dekker, Inc., New York (1991)
Rao, M.M., Ren, Z.D.: Applications of Orlicz Spaces. Monographs and Textbooks in Pure and Applied Mathematics, vol. 250, Marcel Dekker, Inc., New York (2002)
Rychkov, V.S: On a theorem of Bui, Paluszyński, and Taibleson. (Russian) Tr. Mat. Inst. Steklova 227, 286–298 (1999) [translation in Proc. Steklov Inst. Math. 227, 280–292 (1999)]
Sawano, Y.: Wavelet characterization of Besov–Morrey and Triebel–Lizorkin–Morrey spaces. Funct. Approx. Comment. Math. 38, 93–107 (2008)
Sawano, Y., Tanaka, H.: Decompositions of Besov–Morrey spaces and Triebel–Lizorkin–Morrey spaces. Math. Z. 257, 871–905 (2007)
Sawano, Y., Tanaka, H.: Besov–Morrey spaces and Triebel–Lizorkin-Morrey spaces for non-doubling measures. Math. Nachr. 282, 1788–1810 (2009)
Sawano, Y., Yang, D., Yuan, W.: New applications of Besov-type and Triebel–Lizorkin-type spaces. J. Math. Anal. Appl. 363, 73–85 (2010)
Sickel, W., Skrzypczak, L., Vybíral, J.: Complex interpolation of weighted Besov- and Lizorkin–Triebel spaces. Acta Math. Sin. (Engl. Ser.). arXiv:1212.1614 (2012)
Tang, C.: A note on weighted Besov-type and Triebel–Lizorkin-type spaces. J. Funct. Spaces Appl. Article ID 865835 (2013)
Tang, L., Xu, J.: Some properties of Morrey type Besov–Triebel spaces. Math. Nachr. 278, 904–917 (2005)
Triebel, H.: Interpolation Theory, Function Spaces, Differential Operators, 2nd edn. Johann Ambrosius Barth, Heidelberg (1995)
Triebel, H.: Theory of Function Spaces III. Birkhäuser Verlag, Basel (2006)
Ullrich, T.: Continuous characterization of Besov–Lizorkin–Triebel space and new interpretations as coorbits. J. Funct. Space Appl. Article ID 163213 (2012)
Xu, J.: Variable Besov and Triebel–Lizorkin spaces. Ann. Acad. Sci. Fenn. Math. 33, 511–522 (2008)
Xu, J.: The relation between variable Bessel potential spaces and Triebel–Lizorkin spaces. Integral Transf. Spec. Funct. 19, 599–605 (2008)
Yang, D., Yang, S.: Weighted local Orlicz–Hardy spaces with applications to pseudo-differential operators. Dissertationes Math. (Rozprawy Mat.) 478, 1–78 (2011)
Yang, D., Yang, S.: Local Hardy spaces of Musielak–Orlicz type and their applications. Sci. China Math. 55, 1677–1720 (2012)
Yang, D., Yang, S.: Musielak-Orlicz Hardy spaces associated with operators and their applications. J. Geom. Anal. doi: 10.1007/s12220-012-9344-y . arXiv:1201.5512 (2012)
Yang, D., Yuan, W.: A new class of function spaces connecting Triebel–Lizorkin spaces and $$Q$$ spaces. J. Funct. Anal. 255, 2760–2809 (2008)
Yang, D., Yuan, W.: New Besov-type spaces and Triebel–Lizorkin-type spaces including $$Q$$ spaces. Math. Z. 265, 451–480 (2010)
Yang, D., Yuan, W.: Characterizations of Besov-type and Triebel–Lizorkin-type spaces via maximal functions and local means. Nonlinear Anal. 73, 3805–3820 (2010)
Yang, D., Yuan, W.: Dual properties of Triebel–Lizorkin-type spaces and their applications. Z. Anal. Anwend. 30, 29–58 (2011)
Yang, D., Yuan, W.: Relations among Besov-type spaces, Triebel–Lizorkin-type spaces and generallized Carleson measure spaces. Appl. Anal. 92, 549–561 (2013)
Yang, D., Yuan, W., Zhuo, C.: Fourier multipliers on Triebel-Lizorkin-type spaces. J. Funct. Spaces Appl. Article ID 431016 (2012)
Yang, D., Yuan, W., Zhuo, C.: Complex interpolation on Besov-type and Triebel–Lizorkin-type spaces. Anal. Appl. (to appear)