Let X be a compact subset of the complex plane C. We denote by R0(X) the algebra consisting of the (restrictions to X of) rational functions with poles off X. Let m denote 2-dimensional Lebesgue measure. For/» > 1, let L"(X) = L"(X, dm). The closure of R0(X) in LP(X) will be denoted by Rr(X). Whenever p and q both appear, we assume that \/p + \/q = 1. If x is a point in X which admits a bounded...

We study the so-called Skorokhod reflection problem (SRP) posed for real-valued functions defined on a partially ordered set (poset), when there are two boundaries, considered also to be functions of the poset. The problem is to constrain the function between the boundaries by adding and subtracting nonnegative nondecreasing (NN) functions in the most efficient way. We show existence and unique...