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This paper is a continuation of the recent paper of the author, where a certain reproducing kernel Hilbert space \(X_{\mathcal {S}}\) was constructed. The norm in \(X_{\mathcal {S}}\) is related to a certain generalized isoperimetric inequality in \({{\mathbb {R}}^2}\). In the present paper we give an alternative description 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 $$H^{1}[a,b]$$ H 1 [ a , b ]