Bernstein-Szegö inequalities in reproducing kernel hilbert spaces

Let s and t be bounded linear operators from a hilbert space h into a reproducing kernel hilbert space k{cyrillic} of complex or real-valued functions defined on some set k. for each χ ∈ χ,let k χ ∈ k{cyrillic} have the property that <g,k χ>=g(χ) for each g ∈ k. using bessel's inequality,we obtain a sharp estimate relating sf (χ),tf(χ),s*k χand t*k χ this estimate is then applied to obtain bernstein-szegö inequalities for fourier multiplier operators on sobolev spaces in l*.