Geodesic
Description of weak-type BMO-regularity
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 50, Tome 512 (2022), pp. 173-190 Cet article a éte moissonné depuis la source Math-Net.Ru

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The weak-type BMO-regularity property for couples of quasi-Banach lattices of measurable functions was recently introduced as a suitable substitute for the usual BMO-regularity in connection with characterization of the $K$-closedness of Hardy-type spaces on the unit circle and stability for the real interpolation. It was characterized in terms of the BMO-regularity of couples $\left((X, Y)_{\alpha, p}, (X, Y)_{\beta, q}\right)$, $0 < \alpha < \beta < 1$, of the real interpolation spaces. In the present note, a natural characterization of this property similar to that of BMO-regularity for couples of Banach lattices $(X, Y)$ in terms of the BMO-regularity of $X' Y$ is extended to couples of lattices of measurable functions on homogeneous type spaces. We also derive equivalent conditions corresponding to the limit case where $\alpha = 0$. 
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D. V. Rutsky. Description of weak-type BMO-regularity. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 50, Tome 512 (2022), pp. 173-190. http://geodesic.mathdoc.fr/item/ZNSL_2022_512_a9/

[1] J. Bergh, J. Löfström, Interpolation spaces. An introduction, Springer-Verlag, 1976 | MR

[2] M. Cwikel, Y. Sagher, “Relations between real and complex interpolation spaces”, Indiana Univ. Math. J., 36:4 (1987), 905–912 | DOI | MR

[3] F. Cobos, T. Schonbek, “On a theorem by Lions and Peetre about interpolation between a Banach space and its dual”, Houston J. Math., 24:2 (1998), 325–344 | MR

[4] N. J. Kalton, “Complex interpolation of Hardy-type subspaces”, Math. Nachr., 171 (1995), 227–258 | DOI | MR

[5] S. V. Kisliakov, “Interpolation of $H_p$-spaces: some recent developments”, Israel Math. Conf., 13 (1999), 102–140 | MR

[6] S. V. Kislyakov, “On BMO-regular couples of lattices of measurable functions”, Stud. Math., 159:2 (2003), 277–289 | DOI | MR

[7] D. V. Rutsky, “Real Interpolation of Hardy-type Spaces and BMO-regularity”, J. Fourier Anal. Appl., 26:4 (2020), 1–40 | DOI | MR

[8] L. V. Kantorovich, G. P. Akilov, Funktsionalnyi analiz, 4-e izd., Nevskii Dialekt; BKhV-Peterburg, 2004 | MR

[9] S. V. Kislyakov, “O VMO-regulyarnykh reshetkakh izmerimykh funktsii”, Algebra i analiz, 14:2 (2002), 117–135

[10] D. V. Rutskii, “Zamechaniya o BMO-regulyarnosti i AK-ustoichivosti”, Zap. nauchn. semin. POMI, 376, 2010, 116–165

[11] D. V. Rutskii, “BMO-regulyarnost v reshetkakh izmerimykh funktsii na prostranstvakh odnorodnogo tipa”, Algebra i Analiz, 23:2 (2011), 248–295 | MR

[12] D. V. Rutskii, “Veschestvennaya interpolyatsiya prostranstv tipa Khardi: anons i nekotorye zamechaniya”, Zap. nauchn. semin. POMI, 480, 2019, 170–190

[13] D. V. Rutskii, “Vesovaya BMO-regulyarnost slabogo tipa”, Zap. nauchn. semin. POMI, 503, 2021, 97–112