JournalsrmiVol. 28, No. 4pp. 1035–1060

On Hardy spaces associated with certain Schrödinger operators in dimension 2

  • Jacek Dziubański

    Uniwersytet Wrocławski, Wroclaw, Poland
  • Jacek Zienkiewicz

    Uniwersytet Wrocławski, Wroclaw, Poland
On Hardy spaces associated with certain Schrödinger operators in dimension 2 cover
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Abstract

We study the Hardy space H1H^1 associated with the Schrödinger operator L=Δ+VL=-\Delta +V on R2\mathbb R^2, where V0V\geq 0 is a compactly supported non-zero C2C^2-potential. We prove that this space, which is originally defined by means of the maximal function associated with the semigroup generated by L-L, admits a special atomic decomposition with atoms satisfying a~weighted cancellation condition with a weight of logarithmic growth.

Cite this article

Jacek Dziubański, Jacek Zienkiewicz, On Hardy spaces associated with certain Schrödinger operators in dimension 2. Rev. Mat. Iberoam. 28 (2012), no. 4, pp. 1035–1060

DOI 10.4171/RMI/702