# Partial retractions for weighted Hardy spaces

Studia Mathematica (2000)

- Volume: 138, Issue: 3, page 251-264
- ISSN: 0039-3223

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topKisliakov, Sergei, and Xu, Quanhua. "Partial retractions for weighted Hardy spaces." Studia Mathematica 138.3 (2000): 251-264. <http://eudml.org/doc/216703>.

@article{Kisliakov2000,

abstract = {Let 1 ≤ p ≤ ∞ and let $w_0, w_1$ be two weights on the unit circle such that $log(w_0w_1^\{-1\})∈ BMO$. We prove that the couple $(H_p(w_0), H_p(w_1))$ of weighted Hardy spaces is a partial retract of $(L_p(w_0), L_p(w_1))$. This completes previous work of the authors. More generally, we have a similar result for finite families of weighted Hardy spaces. We include some applications to interpolation.},

author = {Kisliakov, Sergei, Xu, Quanhua},

journal = {Studia Mathematica},

keywords = {partial retraction; interpolation; weighted Hardy space; BMO; Hardy space; weight},

language = {eng},

number = {3},

pages = {251-264},

title = {Partial retractions for weighted Hardy spaces},

url = {http://eudml.org/doc/216703},

volume = {138},

year = {2000},

}

TY - JOUR

AU - Kisliakov, Sergei

AU - Xu, Quanhua

TI - Partial retractions for weighted Hardy spaces

JO - Studia Mathematica

PY - 2000

VL - 138

IS - 3

SP - 251

EP - 264

AB - Let 1 ≤ p ≤ ∞ and let $w_0, w_1$ be two weights on the unit circle such that $log(w_0w_1^{-1})∈ BMO$. We prove that the couple $(H_p(w_0), H_p(w_1))$ of weighted Hardy spaces is a partial retract of $(L_p(w_0), L_p(w_1))$. This completes previous work of the authors. More generally, we have a similar result for finite families of weighted Hardy spaces. We include some applications to interpolation.

LA - eng

KW - partial retraction; interpolation; weighted Hardy space; BMO; Hardy space; weight

UR - http://eudml.org/doc/216703

ER -

## References

top- [1] J. Bergh and J. Löfström, Interpolation Spaces, Springer, Berlin, 1976. Zbl0344.46071
- [2] Yu. A. Brudnyi and N. Ya. Krugljak, Real Interpolation Functors and Interpolation Spaces I, North-Holland, 1991.
- [3] F. Cobos and J. Peetre, Interpolation of compact operators: the multidimensional case, Proc. London Math. Soc. 63 (1991), 371-400. Zbl0702.46047
- [4] R. Coifman, M. Cwikel, R. Rochberg, Y. Sagher and G. Weiss, A theory of complex interpolation for families of Banach spaces, Adv. Math. 43 (1982), 203-229. Zbl0501.46065
- [5] M. Cwikel, J. E. McCarty and T. H. Wolff, Interpolation between weighted Hardy spaces, Proc. Amer. Math. Soc. 116 (1992), 381-388.
- [6] S. Janson, Interpolation of subcouples and quotient couples, Ark. Mat. 31 (1993), 307-338. Zbl0803.46080
- [7] N. Kalton, Complex interpolation of Hardy-type subspaces, Math. Nachr. 171 (1995), 227-258. Zbl0837.46015
- [8] S. V. Kisliakov, Interpolation of ${H}^{p}$-spaces: some recent developments, in: Function Spaces, Interpolation Spaces, and Related Topics, Israel Math. Conf. Proc. 13, Bar-Ilan Univ., Ramat Gan, 1999, 102-140. Zbl0956.46018
- [9] S. V. Kisliakov, Bourgain's analytic projection revisited, Proc. Amer. Math. Soc. 126 (1998), 3307-3314. Zbl0902.30025
- [10] S. V. Kisliakov and Q. Xu, Interpolation of Hardy spaces, Trans. Amer. Math. Soc. 343 (1994), 1-34. Zbl0806.46026
- [11] S. V. Kisliakov and Q. Xu, Real interpolation and singular integrals, St. Petersburg Math. J. 8 (1997), 593-615.
- [12] G .Pisier, Interpolation between ${H}^{p}$ spaces and non-commutative generalizations, I, Pacific J. Math. 155 (1992), 341-368. Zbl0747.46050
- [13] Q. Xu, Notes on interpolation of Hardy spaces, Ann. Inst. Fourier (Grenoble) 42 (1992), 875-889; Erratum, 43 (1993), 569. Zbl0760.46060
- [14] Q. Xu, New results on interpolation of Hardy spaces, in: Banach Space Theory and its Applications (Wuhan, 1994), Wuhan Univ. Press, 1996, 13-31.

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