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pro vyhledávání: '"Vuorinen, Emil"'
Autor:
Vuorinen, Emil
The purpose of this note is to prove that the strong Christ-Goldberg maximal function is bounded. This is a matrix weighted maximal operator appearing in the theory of matrix weighted norm inequalities. Related to this we record the Rubio de Francia
Externí odkaz:
http://arxiv.org/abs/2306.03858
Zygmund dilations are a group of dilations lying in between the standard product theory and the one-parameter setting - in $\mathbb{R}^3 = \mathbb{R} \times \mathbb{R} \times \mathbb{R}$ they are the dilations $(x_1, x_2, x_3) \mapsto (\delta_1 x_1,
Externí odkaz:
http://arxiv.org/abs/2203.15777
We study singular integral operators with kernels that are more singular than standard Calder\'on-Zygmund kernels, but less singular than bi-parameter product Calder\'on-Zygmund kernels. These kernels arise as restrictions to two dimensions of certai
Externí odkaz:
http://arxiv.org/abs/2203.15740
Autor:
Vuorinen, Emil
Publikováno v:
In Advances in Mathematics September 2024 453
We prove genuinely multilinear weighted estimates for singular integrals in product spaces. The estimates complete the qualitative weighted theory in this setting. Such estimates were previously known only in the one-parameter situation. Extrapolatio
Externí odkaz:
http://arxiv.org/abs/2011.04459
We present a framework based on modified dyadic shifts to prove multiple results of modern singular integral theory under mild kernel regularity. Using new optimized representation theorems we first revisit a result of Figiel concerning the UMD-exten
Externí odkaz:
http://arxiv.org/abs/2006.05807
We complete our theory of weighted $L^p(w_1) \times L^q(w_2) \to L^r(w_1^{r/p} w_2^{r/q})$ estimates for bilinear bi-parameter Calder\'on--Zygmund operators under the assumption that $w_1 \in A_p$ and $w_2 \in A_q$ are bi-parameter weights. This is d
Externí odkaz:
http://arxiv.org/abs/1910.12546
We prove that the class of trilinear multiplier forms with singularity over a one dimensional subspace, including the bilinear Hilbert transform, admit bounded $L^p$-extension to triples of intermediate $\mathrm{UMD}$ spaces. No other assumption, for
Externí odkaz:
http://arxiv.org/abs/1909.07236
We develop a general theory of multilinear singular integrals with operator-valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multilinear variants of the $\mathcal R$-boundedness condition naturally ar
Externí odkaz:
http://arxiv.org/abs/1908.07233
We prove $L^p$ bounds for the extensions of standard multilinear Calder\'on-Zygmund operators to tuples of UMD spaces tied by a natural product structure. This can, for instance, mean the pointwise product in UMD function lattices, or the composition
Externí odkaz:
http://arxiv.org/abs/1905.02139