Boundary value problems for analytic functions in the class of Cauchy-type integrals with density in

We study the Riemann boundary value problem , for analytic functions in the class of analytic functions represented by the Cauchy-type integrals with density in the spaces with variable exponent. We consider both the case when the coefficient is piecewise continuous and it may be of a more general nature, admitting its oscillation. The explicit formulas for solutions in the variable exponent setting are given. The related singular integral equations in the same setting are also investigated. As an application there is derived some extension of the Szegö-Helson theorem to the case of variable exponents.

Repply to: Brito, A.C., Brotas, V., Caetano, M., Coutinho, T.P., Bordalo, A.A., Icely, J., Neto, J.M., Serôdio, J., Moita, T. (2012) "Defining phytoplankton class boundaries in Portuguese transitional waters: an evaluation of the ecological quality status according to the Water Framework Directive" [Ecological Indicators 19, 5-14]

We write to comment on the recently published paper “Defining phytoplankton class boundaries in Portuguese transitional waters: an evaluation of the ecological quality status according to the Water Framework Directive” (Brito et al., 2012). This paper presents an integrated methodology to analyse the ecological quality status of several Portuguese transitional waters, using phytoplanktonrelated metrics. One of the systems analysed, the Guadiana estuary in southern Portugal, is considered the most problematic estuary, with its upstream water bodies classified as Poor in terms of ecological status. We strongly disagree with this conclusion and we would like to raise awareness to some methodological constraints that, in our opinion, are the basis of such deceptive conclusions and should therefore not be neglected when using phytoplankton to assess the ecological status of natural waters.