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This paper is a continuation of the recent paper of the author, where acertain reproducing kernel Hilbert space $X_{\mathcal{S}}$ was constructed. Thenorm in $X_{\mathcal{S}}$ is related to a certain generalized isoperimetricinequality in ${\mathbb R^2}$. In the present paper we give an alternativedescription of the space $X_{\mathcal{S}}$, which appears to be a Sobolev space$H^{1}[a,b]$ with some special norm.

Some particular norm in the Sobolev space $H^{1}[a,b].$