Norm Inequalities for Mellin Convolutions and their Applications

Norm inequalities for new convolutions and their applications

“…Motivated by these works, in this paper we would like to combine the methods suggested by authors in [14] and [15] with the ideas of Castro and Saitoh in [3] to introduce some new convolution norm inequalities which generalize some results given in [3] and [14]. We also demonstrate the usefulness of our results to derive the boundedness of Hardy and Meijer transforms and obtain L p −weighted estimates for solutions of certain differential equations.…”

“…Quite recently, in view of Hölder's inequality the authors [14] obtained some norm inequalities for Mellin convolutions which have been successfully implemented in many L p −weighted estimates for integral transforms and solutions of partial differential equations.…”

On fractional convolutions and distributions

“…Next, in a series of papers [13][14][15][16][17] (see also [18][19][20][21]), Nhan et al considered a different generalization of the standard convolution, denoted by * ϕ , defined by…”

Various Inequalities in Reproducing Kernel Hilbert Spaces

“…From (1.2), various norm inequalities (see [7,14,15,16,17,18,19]) in reproducing kernel Hilbert spaces were obtained, which were generalized and reproved using various technics and were expanded for various directions with applications to inverse problems and partial differential equations (see [1,4,5,6,8,10,11,9,12,13]).…”