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The paper is devoted to theL  p    ${L^{p}}$   -theory of boundary integral operators for boundary value problems described by anisotropic Helmholtz operators with variable coefficients in unbounded domains with unbounded smooth boundary. We prove the invertibility of boundary integral operators for Dirichlet and Neumann problems in the Bessel-potential spacesH   s  ,  p    ⁢   (   ∂  ⁡  D   )${H^{s,p}(\partial D)}$   ,p  ∈   (  1  ,  ∞  )${p\in(1,\infty)}$   , and the Besov spacesB   p  ,  q   s   ⁢   (   ∂  ⁡  D   )${B_{p,q}^{s}(\partial D)}$   ,p  ,  q   ∈   [  1  ,  ∞  ]${p,q\in[1,\infty]}$   . We prove also the Fredholmness of the Robin problem in these spaces and give the index formula.

L p -theory of boundary integral operators for domains with unbounded smooth boundary