TY - JOUR

T1 - The Brown–Halmos theorem for a pair of abstract Hardy spaces

AU - Karlovich, Alexei

AU - Shargorodsky, Eugene

N1 - info:eu-repo/grantAgreement/FCT/5876/147204/PT#
sem pdf conforme despacho.

PY - 2018

Y1 - 2018

N2 - Let H[X] and H[Y] be abstract Hardy spaces built upon Banach function spaces X and Y over the unit circle T. We prove an analogue of the Brown–Halmos theorem for Toeplitz operators Ta acting from H[X] to H[Y] under the only assumption that the space X is separable and the Riesz projection P is bounded on the space Y. We specify our results to the case of variable Lebesgue spaces X=Lp(⋅) and Y=Lq(⋅) and to the case of Lorentz spaces X=Y=Lp,q(w), 1p(T).

AB - Let H[X] and H[Y] be abstract Hardy spaces built upon Banach function spaces X and Y over the unit circle T. We prove an analogue of the Brown–Halmos theorem for Toeplitz operators Ta acting from H[X] to H[Y] under the only assumption that the space X is separable and the Riesz projection P is bounded on the space Y. We specify our results to the case of variable Lebesgue spaces X=Lp(⋅) and Y=Lq(⋅) and to the case of Lorentz spaces X=Y=Lp,q(w), 1p(T).

KW - Banach function space

KW - Brown–Halmos theorem

KW - Pointwise multiplier

KW - Toeplitz operator

KW - Variable Lebesgue space

KW - Weighted Lorentz space

UR - http://www.scopus.com/inward/record.url?scp=85056634900&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2018.11.022

DO - 10.1016/j.jmaa.2018.11.022

M3 - Article

AN - SCOPUS:85056634900

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

ER -