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1 results

  • FREDHOLM THEORY OF TOEPLITZ OPERATORS ON THE HARDY SPACE $H^1$

  • J. A. VIRTANEN
  • Journal:
    Bulletin of the London Mathematical Society / Volume 38 / Issue 1 / February 2006
    Published online by Cambridge University Press:
    30 January 2006, pp. 143-155
    Print publication:
    February 2006

  • The Fredholm properties of Toeplitz operators $T_a$ on Hardy spaces $H^p$ ($1<p<\infty$) with continuous symbols $a$ are well understood. We consider $T_a$ acting on $H^1$, where the operator is bounded provided that $a$ belongs to the class of symbols given by Janson and Stegenga's result on the pointwise multipliers on $H^1$. A necessary and sufficient condition for $T_a$ to be a Fredholm operator is given when $a$ is continuous and satisfies a mild additional condition (much weaker than Hölder continuity). A formula for the index of $T_a$ is also derived. In addition, we study the case of matrix-valued symbols and Toeplitz operators on $\rm{BMO}_A$.