On the H–l Boundedness of Operators
نویسنده
چکیده
We prove that if q is in (1,∞), Y is a Banach space, and T is a linear operator defined on the space of finite linear combinations of (1, q)-atoms in R with the property that sup{‖Ta‖Y : a is a (1, q)-atom} < ∞, then T admits a (unique) continuous extension to a bounded linear operator from H(R) to Y . We show that the same is true if we replace (1, q)-atoms by continuous (1,∞)-atoms. This is known to be false for (1,∞)-atoms.
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