Abstract
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 $T_a$ 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 $X=L^{p(\cdot)}$ and $Y=L^{q(\cdot)}$ and to
the case of Lorentz spaces $X=Y=L^{p,q}(w)$, $1<p<\infty$, $1\le q<\infty$
with Muckenhoupt weights $w\in A_p(\T)$.
Original language | English |
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Pages (from-to) | 246-265 |
Number of pages | 20 |
Journal | Journal of Mathematical Analysis and Applications |
Volume | 472 |
Issue number | 1 |
Early online date | 13 Nov 2018 |
DOIs | |
Publication status | Published - Apr 2019 |
Keywords
- Banach function space
- Brown–Halmos theorem
- Pointwise multiplier
- Toeplitz operator
- Variable Lebesgue space
- Weighted Lorentz space