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Title of Journal: Math Z

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Abbravation: Mathematische Zeitschrift

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Springer Berlin Heidelberg

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DOI

10.1016/0306-3747(94)90381-6

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1432-1823

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On Hörmander’s solution of the barpartial

Authors: Haakan Hedenmalm
Publish Date: 2015/05/26
Volume: 281, Issue: 1-2, Pages: 349-355
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Abstract

We explain how Hörmander’s classical solution of the barpartial equation in the plane with a weight which permits growth near infinity carries over to the rather opposite situation when we ask for decay near infinity Here however a natural condition on the datum needs to be imposed The condition is not only natural but also necessary to have the result at least in the Fock weight case The norm identity which leads to the estimate is related to general areatype results in the theory of conformal mappingsThe author wishes to thank Ioannis Parissis and Serguei Shimorin 14 for stimulating discussions related to the norm identity 21 The author also wishes to thank Grigori Rozenblum for an enlightening conversion on the topic of this paper at the Euler Institute in StPetersburg in July 2013

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  2. Stable reduction of curves and tame ramification
  3. Constant mean curvature graphs on exterior domains of the hyperbolic plane
  4. On weighted critical imbeddings of Sobolev spaces
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  10. Real K 3 surfaces without real points, equivariant determinant of the Laplacian, and the Borcherds Φ-function
  11. Positive semidefinite diagonal minus tail forms are sums of squares
  12. On the measures of large entropy on a positive closed current
  13. Fano varieties in index one Fano complete intersections
  14. Families over special base manifolds and a conjecture of Campana
  15. On the holomorphic structure of G -orbits in compact hermitian symmetric spaces
  16. Derivations, the Lawrence–Sullivan interval and the Fiorenza–Manetti mapping cone
  17. On the geometry of model almost complex manifolds with boundary
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  19. Injectivity radius and diameter of the manifolds of flags in the projective planes
  20. On the invariant distributions of $$C^2$$ circle diffeomorphisms of irrational rotation number
  21. Capillary surfaces in a convex cone
  22. Harmonic maps of finite uniton number into G 2
  23. On characteristic twists of multiple Dirichlet series associated to Siegel cusp forms
  24. On irregular binomial D -modules
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  26. Harmonicity of sections of sphere bundles
  27. Cluster categories of type $${\mathbb {A}}_\infty ^\infty $$ and triangulations of the infinite strip
  28. A lower bound on Seshadri constants of hyperplane bundles on threefolds
  29. Saturated fusion systems over $$\mathcal {A}_2$$-groups
  30. Collapsing sequences of solutions to the Ricci flow on 3-manifolds with almost nonnegative curvature
  31. On newforms for Kohnen plus spaces
  32. Cumulants in noncommutative probability theory I. Noncommutative exchangeability systems
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  34. Distributional chaos for operators with full scrambled sets
  35. Packing dimension and Ahlfors regularity of porous sets in metric spaces
  36. Invariance de la Γ-dimension pour certaines familles kählériennes de dimension 3
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  41. Restriction to symmetric subgroups of unitary representations of rank one semisimple Lie groups
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