Now showing items 1-7 of 7

    • Bilinear Calderón--Zygmund theory on product spaces 

      Li, K.; Martikainen, H.; Vuorinen, E. (2019-10)
      We develop a wide general theory of bilinear bi-parameter singular integrals $T$. This includes general Calder\'on--Zygmund type principles in the bilinear bi-parameter setting: easier bounds, like estimates in the Banach ...
    • Bilinear representation theorem 

      Li, K.; Martikainen, H.; Ou, Y.; Vuorinen, E. (2018-01-01)
      We represent a general bilinear Calderón--Zygmund operator as a sum of simple dyadic operators. The appearing dyadic operators also admit a simple proof of a sparse bound. In particular, the representation implies a so ...
    • Bloom type inequality for bi-parameter singular integrals: efficient proof and iterated commutators 

      Li, K.; Martikainen, H.; Vuorinen, E. (2019-03-14)
      Utilising some recent ideas from our bilinear bi-parameter theory, we give an efficient proof of a two-weight Bloom type inequality for iterated commutators of linear bi-parameter singular integrals. We prove that if $T$ ...
    • Bloom type upper bounds in the product BMO setting 

      Li, K.; Martikainen, H.; Vuorinen, E. (2019-04-08)
      We prove some Bloom type estimates in the product BMO setting. More specifically, for a bounded singular integral $T_n$ in $\mathbb R^n$ and a bounded singular integral $T_m$ in $\mathbb R^m$ we prove that $$ \| [T_n^1, ...
    • End-point estimates, extrapolation for multilinear muckenhoupt classes, and applications 

      Li, K.; Martell, J.M.; Martikainen, H.; Ombrosi, S.; Vuorinen, E. (2019)
      In this paper we present the results announced in the recent work by the first, second, and fourth authors of the current paper concerning Rubio de Francia extrapolation for the so-called multilinear Muckenhoupt classes. ...
    • Multilinear operator-valued calderón-zygmund theory 

      Di Plinio, F.; Li, K.; Martikainen, H.; Vuorinen, E. (2020)
      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 R-boundedness ...
    • Multilinear singular integrals on non-commutative lp spaces 

      Di Plinio, F.; Li, K.; Martikainen, H.; Vuorinen, E. (2019)
      We prove Lp bounds for the extensions of standard multilinear Calderón- Zygmund operators to tuples of UMD spaces tied by a natural product structure. The product can, for instance, mean the pointwise product in UMD ...