# A note on Carleson measures for Hardy spaces

La Blasco Cruz, O; Jarchow, H (2005). A note on Carleson measures for Hardy spaces. Acta Universitatis Szegediensis. Acta Scientiarum Mathematicarum, 71(1-2):371-389.

## Abstract

We investigate Carleson measures µ on D where D is the open unit disk in C, along with functional analytic properties of the formal identitiy of the Hardy space H p (D) into the Lebesgue space Lq (µ), for any previously ﬁxed 0 < p, q <
∞. Our corresponding characterizations do not only extend the classical results for measures concentrated on D but also provide diﬀerent proofs for the latter ones. Among the
applications are generalizations to formal identities as above of several results which have been known for composition operators only.

## Abstract

We investigate Carleson measures µ on D where D is the open unit disk in C, along with functional analytic properties of the formal identitiy of the Hardy space H p (D) into the Lebesgue space Lq (µ), for any previously ﬁxed 0 < p, q <
∞. Our corresponding characterizations do not only extend the classical results for measures concentrated on D but also provide diﬀerent proofs for the latter ones. Among the
applications are generalizations to formal identities as above of several results which have been known for composition operators only.

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