Komla Domelevo

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math.FA2023

The dyadic Riesz vector II

Komla Domelevo, Stefanie Petermichl

We derive a dyadic model operator for the Riesz vector. We show linear upper $L^{p}$ bounds for $1 < p < \infty$ between this model operator and the Riesz vector, when applied to fun…

math.FA2023

The dyadic Riesz vector I

Komla Domelevo, Stefanie Petermichl

We derive a dyadic model operator for the Riesz vector. We show linear lower $L^{p}$ bounds for $1 < p < \infty$ between this model operator and the Riesz vector, when applied to fun…

math.FA2023

The dyadic and the continuous Hilbert transforms with values in Banach spaces. Part2

Komla Domelevo, Stefanie Petermichl

We show that if the dyadic Hilbert transform with values in a Banach space is $L^{p}$ bounded, then so is the Hilbert transform, with a linear relation of the bounds. This result is…