engleski

Multidimensional Hilbert-type inequalities obtained via local fractional calculus

In this paper we give a unified treatment of multidimensional fractal Hilbert-type inequalities. More precisely, we establish a Hilbert-type inequality with a general local fractional continuous kernel and weight functions. A particular emphasis is dedicated to a class of inequalities with a homogeneous kernel. Namely, we impose some weak conditions for which the constants appearing on the right-hand sides of such Hilbert-type inequalities are the best possible. As an application, we discuss some particular choices of homogeneous kernels and power weight functions.

Hilbert inequality ; conjugate parameters ; homogeneous function ; local fractional calculus ; multidimensional form

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