Real interpolation of weighted tent spaces

References

• Coifman RR, Meyer Y, Stein EM. Un nouvel éspace fonctionnel adapté à l’étude des opérateurs définis par des intégrales singulières [A new function space suitable for the study of operators defined by singular integrals]. In: Mauceri G, Ricci F, Weiss G, editors. Harmonic analysis (Cortona, 1982). Vol. 992, Lecture notes in mathematics. Berlin: Springer; 1983. p. 1–15.
   Google Scholar
• Coifman RR, Meyer Y, Stein EM. Some new function spaces and their applications to harmonic analysis. J. Funct. Anal. 1985;62:304–335.
   Web of Science ®Google Scholar
• Welland G, Zhao S. ε-families of operators in Triebel-Lizorkin and tent spaces. Canad. J. Math. 1995;47:1095–1120.
   Web of Science ®Google Scholar
• Duong XT, Yan L. New function spaces of BMO type, the John-Nirenberg inequality, interpolation, and applications. Comm. Pure Appl. Math. 2005;58:1375–1420.
   Web of Science ®Google Scholar
• Long R. Real interpolation of tent spaces on product domains. Acta Math. Sinica. 1987;30:492–503. Chinese.
   Google Scholar
• Bonami A, Johnson R. Tent spaces based on the Lorentz spaces. Math. Nachr. 1987;132:81–99.
   Web of Science ®Google Scholar
• Alvarez J, Milman M. Interpolation of tent spaces and applications. In: Cwikel M, Peetre J, Sagher Y, Wallin H, editors. Function spaces and applications (Lund, 1986). Vol. 1302, Lecture notes in mathematics. Berlin: Springer; 1988. p. 11–21.
   Google Scholar
• Alvarez J, Milman M. Spaces of Carleson measures: duality and interpolation. Ark. Mat. 1987;25:155–174.
   Web of Science ®Google Scholar
• Soria J. Weighted tent spaces. Math. Nachr. 1992;155:231–256.
   Web of Science ®Google Scholar
• Amar É, Bonami A. Mesures de Carleson d’ordre α et solutions au bord de l’équation ⁻∂ [Carleson measures of order α and boundary solutions of the equation ∂]. Bull. Soc. Math. France. 1979;107:23–48.
   Google Scholar
• Russ E. The atomic decomposition for tent spaces on spaces of homogeneous type. In: McIntosh A, Portal P, editors. CMA/AMSI Research Symposium “Asymptotic Geometric Analysis, Harmonic Analysis, and Related Topics”. Vol. 42, Proceedings of the Centre for Mathematical Analysis, The Australian National University. Canberra: Australian National University; 2007. p. 125–135.
   Google Scholar
• Amenta A. Tent spaces over metric measure spaces under doubling and related assumptions. In: Ball JA, Dritschel MA, ter Elst AFM, Portal P, Potapov D, editors. Operator theory in harmonic and non-commutative analysis. Vol. 240, Operator theory: advances and applications. Cham: Birkhäuser/Springer; 2014. p. 1–29.
   Google Scholar
• Fefferman C, Riviére NM, Sagher Y. Interpolation between H\textsuperscript{p} spaces: the real method. Trans. Amer. Math. Soc. 1974;191:75–81.
   Web of Science ®Google Scholar
• He D. Square function characterization of weak Hardy spaces. J. Fourier Anal. Appl. 2014;20:1083–1110.
   Web of Science ®Google Scholar
• Bui HQ. Weighted Besov and Triebel spaces: interpolation by the real method. Hiroshima Math. J. 1982;12:581–605.
   Google Scholar
• Harboure E, Salinas O, Viviani BE. A look at BMOφ (w) through Carleson measures. J. Fourier Anal. Appl. 2007;13:267–284.
   Web of Science ®Google Scholar
• Soria J. Tent spaces based on weighted Lorentz spaces. Carleson measures [PhD thesis]. Washington University in St. Louis; 1990. 121pp.
   Google Scholar
• Cao J, Chang D-C, Wu H, et al. Weak Hardy spaces WHLp (ℝn) associated to operators satisfying k-Davies-Gaffney estimates. J. Nonlinear Convex Anal. 2015;16:1205–1255.
   Web of Science ®Google Scholar
• Harboure E, Torrea JL, Viviani BE. A vector-valued approach to tent spaces. J. Anal. Math. 1991;56:125–140.
   Web of Science ®Google Scholar
• Fefferman C, Stein EM. H\textsuperscript{p} spaces of several variables. Acta Math. 1972;129:137–193.
   Web of Science ®Google Scholar
• Folland GB, Stein EM. Hardy spaces on homogeneous groups. Vol. 28, Mathematical notes. Princeton (NJ): Princeton University Press; Tokyo: University of Tokyo Press; 1982.
   Google Scholar
• García-Cuerva J. Weighted Hp spaces. Dissertationes Math. (Rozprawy Mat.). 1979;162:1–63.
   Google Scholar
• Strömberg JO, Torchinsky A. Weighted Hardy spaces. Vol. 1381, Lecture notes in mathematics. Berlin: Springer-Verlag; 1989.
   Google Scholar
• Stein EM, Weiss G. On the theory of harmonic functions of several variables. I. The theory of H\textsuperscript{p}-spaces. Acta Math. 1960;103:25–62.
   Web of Science ®Google Scholar
• Abu-Shammala W, Torchinsky A. The Hardy-Lorentz spaces Hp,q(ℝn). Stud. Math. 2007;182:283–294.
   Web of Science ®Google Scholar
• Fefferman R, Soria F. The space weak H\textsuperscript{1}. Stud. Math. 1986;85:1–16.
   Web of Science ®Google Scholar
• Liu H. The weak H\textsuperscript{p} spaces on homogenous groups. In: Cheng M-T, Deng D-G, Zhou X-W, editors. Harmonic analysis (Tianjin, 1988). Vol. 1984, Lecture notes in mathematics. Berlin: Springer; 1991. p. 113–118.
   Google Scholar
• Liang Y, Yang D, Jiang R. Weak Musielak-Orlicz-Hardy spaces and applications. Math. Nachr. 2015; doi: 10.1002/mama.201500152
   Google Scholar
• Janson S, Nilsson P, Peetre J. Notes on Wolff’s note on interpolation spaces. Proc. London Math. Soc. (3). 1984;48:283–299.
   Web of Science ®Google Scholar
• Bergh J, Löfström J. Interpolation spaces. An introduction. Vol. 223, Grundlehren der Mathematischen Wissenschaften. Berlin: Springer-Verlag; 1976.
   Google Scholar
• Bergh J, Cobos F. A maximal description for the real interpolation method in the quasi-Banach case. Math. Scand. 2000;87:22–26.
   Web of Science ®Google Scholar
• Triebel H. Interpolation theory, function spaces, differential operators. 2nd ed. Heidelberg: Johann Ambrosius Barth; 1995.
   Google Scholar
• Cobos F, Peetre J, Persson LE. On the connection between real and complex interpolation of quasi-Banach spaces. Bull. Sci. Math. 1998;122:17–37.
   Web of Science ®Google Scholar
• Kalton N, Mayboroda S, Mitrea M. Interpolation of Hardy-Sobolev-Besov-Triebel-Lizorkin spaces and applications to problems in partial differential equations. In: Carli LD, Milman M, editors. Interpolation theory and applications. Vol. 445, Contemporary mathematics. Providence (RI): American Mathematical Society; 2007. p. 121–177.
   Google Scholar
• Gagliardo E. Una struttura unitaria in diverse famiglie di spazi funzionali. I. Ricerche Mat. 1961;10:244–281.
   Google Scholar
• Janson S. On the interpolation of sublinear operators. Stud. Math. 1982;75:51–53.
   Web of Science ®Google Scholar
• Grafakos L. Classical Fourier analysis. 3rd ed. Vol. 249, Graduate texts in mathematics. New York (NY): Springer; 2014.
   Google Scholar
• Bui TA, Cao J, Ky LD, et al. Weighted Hardy spaces associated with operators satisfying reinforced off-diagonal estimates. Taiwanese J. Math. 2013;17:1127–1166.
   Web of Science ®Google Scholar
• Folland GB. Real analysis. Modern techniques and their applications, pure and applied mathematics (New York). New York (NY): Wiley-Interscience, Wiley; 1984.
   Google Scholar
• Rubio de Francia JL, Ruiz FJ, Torrea JL. Calderón-Zygmund theory for operator-valued kernels. Adv. Math. 1986;62:7–48.
   Web of Science ®Google Scholar
• Stein EM, Weiss G. Introduction to Fourier analysis on Euclidean spaces. Vol. 32, Princeton mathematical series. Princeton (NJ): Princeton University Press; 1971.
   Google Scholar
• Sagher Y. Interpolation of r-Banach spaces. Stud. Math. 1972;41:45–70.
   Web of Science ®Google Scholar
• Cobos F, Fernández-Martínez P. Reiteration and a Wolff theorem for interpolation methods defined by means of polygons. Stud. Math. 1992;102:239–256.
   Web of Science ®Google Scholar