On maximal function of discrete rough truncated Hilbert transforms
We prove the weak type (1,1) estimate for maximal function of the truncated rough Hilbert transform considered in [9] and [10]
math.CA↗
arXiv subjects
Maciej Paluszynski
Publications and source records attributed to Maciej Paluszynski.
Dimension independent atomic decoposition for dyadic martingale $H^1$
We introduce atoms for dyadic atomic $H^1$ for which the equivalence between atomic and maximal function defnitions is dimension independent. We give the sharp, up to $\log(d)$ factor, estimates for the $H^1 \to L^1$ norm estimates for the special maximal function.
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On Inverses of Discrete Rough Hilbert Transforms
We describe the structure of the resolvent of the discrete rough truncated Hilbert transform under the critical exponent. This extends the results obtained in [8].
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Weak type (1,1) estimates for inverses of discrete rough singular integral operators
We obtain weak type (1,1) estimates for the inverses of truncated discrete rough Hilbert transform. We include an ex- ample showing that our result is sharp. One of the ingredients of the proof are regularity estimates for convolution of singular measure associated with the sequence $[m^α]$.
math.FA↗