An operator-valued T(1) theorem for symmetric singular integrals in UMD spaces
نویسندگان
چکیده
The natural BMO (bounded mean oscillation) conditions suggested by scalar-valued results are known to be insufficient for the boundedness of operator-valued paraproducts. Accordingly, singular integrals has only been available under versions classical “T(1)?BMO” assumptions that not easily checkable. Recently, Hong, Liu and Mei (J. Funct. Anal. 2020) observed situation improves remarkably with a symmetry assumption, so T(1) criterion still guarantees their L2-boundedness on Hilbert space -valued functions. Here, these extended general UMD (unconditional martingale differences) spaces same condition symmetrised paraproducts, requiring in addition usual replacement uniform bounds R-bounds case integrals. In particular, assumptions, we obtain non-commutative Lp all 1<p<?, without need replace domain or target related Hardy as Hong et al. p?2.
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2021
ISSN: ['0022-1236', '1096-0783']
DOI: https://doi.org/10.1016/j.jfa.2021.108933