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In this paper, we investigate some reverse weighted Lp -norm ( p > 1) inequalities for convolutions related to Kontorovich-Lebedev, Fourier cosine transforms. A class of intergrodiffirential equations involing in Bessel operator are considered. The estimate of scratted acoustic field is established. Mathematics subject classification (2010): 35A22, 44A35, 26D15, 26D10, 45E10, 45J05, 33E30, 65R10.

On the reverse convolution inequalities for the Kontorovich-Lebedev, Fourier cosine transforms and applications