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- W4301416085 abstract "Let $Gamma$ be a rectifiable Jordan curve, let $X$ and $Y$ be two reflexive Banach function spaces over $Gamma$ such that the Cauchy singular integral operator $S$ is bounded on each of them, and let $M(X,Y)$ denote the space of pointwise multipliers from $X$ to $Y$. Consider the Riesz projection $P=(I+S)/2$, the corresponding Hardy type subspaces $PX$ and $PY$, and the Toeplitz operator $T(a):PXto PY$ defined by $T(a)f=P(af)$ for a symbol $ain M(X,Y)$. We show that if $Xhookrightarrow Y$ and $ain M(X,Y)setminus{0}$, then $T(a)inmathcal{L}(PX,PY)$ has a trivial kernel in $PX$ or a dense image in $PY$. In particular, if $1<qle p<infty$, $1/r=1/q-1/p$, and $ain L^{r}equiv M(L^p,L^q)$ is a nonzero function, then the Toeplitz operator $T(a)$, acting from the Hardy space $H^p$ to the Hardy space $H^q$, has a trivial kernel in $H^p$ or a dense image in $H^q$." @default.
- W4301416085 created "2022-10-05" @default.
- W4301416085 creator A5086357937 @default.
- W4301416085 date "2017-08-04" @default.
- W4301416085 modified "2023-10-18" @default.
- W4301416085 title "The Coburn-Simonenko theorem for Toeplitz operators acting between Hardy type subspaces of different Banach function spaces" @default.
- W4301416085 doi "https://doi.org/10.48550/arxiv.1708.01475" @default.
- W4301416085 hasPublicationYear "2017" @default.
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