# The noncommutative $$H^{(r,s)}_{p}({\mathcal A};\ell _{\infty })$$ H p ( r , s ) ( A ; ℓ ∞ ) and $$H_{p}({\mathcal A};\ell _{1})$$ H p ( A ; ℓ 1 ) spaces

The noncommutative $$H^{(r,s)}_{p}({\mathcal A};\ell _{\infty })$$ H p ( r , s ) ( A ;... In this paper we introduce the noncommutative $$H^{(r,s)}_{p}({\mathcal A};\ell _{\infty })$$ H p ( r , s ) ( A ; ℓ ∞ ) and $$H_{p}({\mathcal A};\ell _{1})$$ H p ( A ; ℓ 1 ) spaces, and prove the contractivity of the underlying conditional expectation $$\varPhi$$ Φ on these spaces. We also give results on duality and complex interpolation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# The noncommutative $$H^{(r,s)}_{p}({\mathcal A};\ell _{\infty })$$ H p ( r , s ) ( A ; ℓ ∞ ) and $$H_{p}({\mathcal A};\ell _{1})$$ H p ( A ; ℓ 1 ) spaces

, Volume 19 (4) – Mar 8, 2015
15 pages

/lp/springer_journal/the-noncommutative-h-r-s-p-mathcal-a-ell-infty-h-p-r-s-a-and-h-p-4RmtsV5kwb
Publisher
Springer Basel
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-015-0332-x
Publisher site
See Article on Publisher Site

### Abstract

In this paper we introduce the noncommutative $$H^{(r,s)}_{p}({\mathcal A};\ell _{\infty })$$ H p ( r , s ) ( A ; ℓ ∞ ) and $$H_{p}({\mathcal A};\ell _{1})$$ H p ( A ; ℓ 1 ) spaces, and prove the contractivity of the underlying conditional expectation $$\varPhi$$ Φ on these spaces. We also give results on duality and complex interpolation.

### Journal

PositivitySpringer Journals

Published: Mar 8, 2015

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