## Vector valued reproducing kernel Hilbert spaces of integrable functions and Mercer theorem.(English)Zbl 1116.46019

The authors study reproducing kernel Hilbert spaces such that their elements are $$p$$-integrable functions. It is shown that this is equivalent to the fact that the integral operator whose kernel is the reproducing kernel is a bounded operator from $$L^{p/(p-1)}$$ to $$L^p$$.

### MSC:

 46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) 47B34 Kernel operators 47G10 Integral operators
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### References:

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