A fractional logarithmic p-Laplacian operator is defined by differentiating the fractional p-Laplacian, yielding an integral form with a log term, and applied to prove inequalities and eigenvalue results.
Milman , On some criteria for the regularity of spaces of the type (B), Comptes Rendus de l'Acad\'emie des Sciences de l'URSS , 20 (4), 243-246, (1938)
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On the fractional logarithmic $p$-Laplacian
A fractional logarithmic p-Laplacian operator is defined by differentiating the fractional p-Laplacian, yielding an integral form with a log term, and applied to prove inequalities and eigenvalue results.