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Generalized Poincaré embeddings and weighted Hardy operator on spaces. (English) Zbl 1201.42015
The well-known Poincaré embedding $\dot{W}^{1,n}(\mathbb{R}^n)\subset \text{BMO}(\mathbb{R}^n)$ and the John-Nirenberg inequality in $\text{BMO}(\mathbb{R}^n)$ are useful tools in modern analysis and partial differential equations. The authors establish the generalized Poincaré embeddings and the John-Nirenberg inequality in the $Q$-type spaces $Q^{\alpha, q}_p(\mathbb{R}^n)$ for all $\alpha \in (0,1)$, $p\in(0,\infty]$ and $q\in[1,\infty]$, which generalizes the corresponding classical results on $\text{BMO}(\mathbb{R}^n)$. Moreover, the authors also give sufficient and necessary conditions on the function $\psi$ to ensure that the corresponding weighted Hardy operator $U_\psi$ and its adjoint, the weighted Cesàro average operator $V_\psi$, are bounded on the spaces $Q^{\alpha, q}_p(\mathbb{R}^n)$.

42B30$H^p$-spaces (Fourier analysis)
46E35Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
42B35Function spaces arising in harmonic analysis
Full Text: DOI
[1] Andersson, M.; Carlsson, H.: Qp spaces in strictly pseudoconvex domains, J. anal. Math. 84, 335-359 (2001) · Zbl 0990.32001 · doi:10.1007/BF02788114
[2] Carton-Lebrun, C.; Fosset, M.: Moyennes et quotients de Taylor dans BMO, Bull. soc. Roy. sci. Liége 53, 85-87 (1984) · Zbl 0543.42013
[3] Cui, L.; Yang, Q.: On the generalized Morrey spaces, Siberian math. J. 46, 133-141 (2005) · Zbl 1096.46015 · emis:journals/SMZ/2005/01/166.htm
[4] Dafni, G.; Xiao, J.: Some new tent spaces and duality theorems for fractional Carleson measures and $Q{\alpha}$(Rn), J. funct. Anal. 208, 377-422 (2004) · Zbl 1062.42011 · doi:10.1016/S0022-1236(03)00181-2
[5] Dafni, G.; Xiao, J.: The dyadic structure and atomic decomposition of Q spaces in several variables, Tohoku math. J. 57, 119-145 (2005) · Zbl 1129.42400 · doi:10.2748/tmj/1113234836
[6] Englis, M.: Qp-spaces: generalizations to bounded symmetric domains, , 53-71 (2005) · Zbl 1121.32010
[7] Essén, M.; Janson, S.; Peng, L.; Xiao, J.: Q spaces of several real variables, Indiana univ. Math. J. 49, 575-615 (2000) · Zbl 0984.46020 · doi:10.1512/iumj.2000.49.1732
[8] Frazier, M.; Jawerth, B.; Weiss, G.: Littlewood-Paley theory and the study on function space, CBMS-AMS regional conference (1989)
[9] John, F.; Nirenberg, L.: On functions of bounded mean oscillation, Comm. pure appl. Math. 18, 415-426 (1965) · Zbl 0102.04302 · doi:10.1002/cpa.3160140317
[10] Latvala, V.: On subclasses of $BMO(B)$ for solutions of quasilinear elliptic equations, Analysis 19, 22-35 (1999) · Zbl 0929.35040
[11] Li, P.; Zhai, Z.: Well-posedness and regularity of generalized Navier-Stokes equations in some critical Q-spaces, (2009) · Zbl 1205.35202
[12] Li, P.; Zhai, Z.: Several analytic inequalities in some Q-spaces, (2009) · Zbl 1239.42025
[13] Li, P.; Zhai, Z.: Riesz transforms on Q-type spaces with application to quasi-geostrophic equation, (2009) · Zbl 1259.35160
[14] Li, P.; Zhai, Z.: Generalized Navier-Stokes equations with initial data in local Q-type spaces, J. math. Anal. appl. 369, 595-609 (2010) · Zbl 1194.35309 · doi:10.1016/j.jmaa.2010.04.006
[15] Peng, L.; Yang, Q.: Predual spaces for Q spaces, Acta math. Sci. 29, 243-250 (2009) · Zbl 1199.46072 · doi:10.1016/S0252-9602(09)60025-4
[16] Pott, S.; Smith, M.: Paraproducts and Hankel operators of Schatten class via p-John-Nirenberg theorem, J. funct. Anal. 217, 37-78 (2004) · Zbl 1089.47024 · doi:10.1016/j.jfa.2004.03.005
[17] Sawano, Y.; Yang, D.; Yuan, W.: New applications of Besov-type and Triebel-Lizorkin-type spaces, J. math. Anal. appl. 363, 73-85 (2010) · Zbl 1185.42022 · doi:10.1016/j.jmaa.2009.08.002
[18] Shatah, J.; Struwe, M.: Geometric wave equations, Courant lect. Notes math. 2 (1998) · Zbl 0993.35001
[19] Wu, Z.; Xie, C.: Decomposition theorems for qp spaces, Ark. mat. 40, No. 2, 383-401 (2002) · Zbl 1043.30017
[20] Xiao, J.: Lp and BMO bounds of weighted Hardy-Littlewood averages, J. math. Anal. appl. 262, 660-666 (2001) · Zbl 1009.42013 · doi:10.1006/jmaa.2001.7594
[21] Xiao, J.: A sharp Sobolev trace inequality for the fractional-order derivatives, Bull. sci. Math. 130, 87-96 (2006) · Zbl 1096.46019 · doi:10.1016/j.bulsci.2005.07.002
[22] Xiao, J.: Homothetic variant of fractional Sobolev space with application to Navier-Stokes system, Dyn. partial differ. Equ. 4, 227-245 (2007) · Zbl 1147.42008
[23] Yang, D.; Yuan, W.: A note on dyadic Hausdorff capacities, Bull. sci. Math. 132, 500-509 (2008) · Zbl 1154.31004 · doi:10.1016/j.bulsci.2007.06.005
[24] Yang, D.; Yuan, W.: A new class of function spaces connecting Triebel-Lizorkin spaces and Q spaces, J. funct. Anal. 255, 2760-2809 (2008) · Zbl 1169.46016 · doi:10.1016/j.jfa.2008.09.005
[25] Yang, D.; Yuan, W.: New Besov-type spaces and Triebel-Lizorkin-type spaces, Math. Z. 265, 451-480 (2010) · Zbl 1191.42011 · doi:10.1007/s00209-009-0524-9
[26] Yuan, W.; Sawano, Y.; Yang, D.: Decompositions of Besov-Hausdorff and Triebel-Lizorkin-Hausdorff spaces and their applications, J. math. Anal. appl. 369, 736-757 (2010) · Zbl 1201.46034 · doi:10.1016/j.jmaa.2010.04.021
[27] Yue, H.; Dafni, G.: A John-Nirenberg type inequality for $Q{\alpha}$(Rn), J. math. Anal. appl. 351, 428-439 (2009) · Zbl 1161.26013 · doi:10.1016/j.jmaa.2008.10.020
[28] Zhai, Z.: Well-posedness for fractional Navier-Stokes equations in critical spaces close to B{ }$\infty ,\infty -(2{\beta}-1)$(Rn), Dyn. partial differ. Equ. 7, 25-44 (2010) · Zbl 1196.35157 · http://intlpress.com/DPDE/journal/DPDE-v07.php