Weighted $L_P-$ Norm Inequalities For Various Convolution Type Transformations And Their Applications

Authors

  • Nguyen Du Vi Nhan Department of Mathematics, Quy Nhon University, Binh Dinh, Vietnam
  • Dinh Thanh Duc Department of Mathematics, Quy Nhon University, Binh Dinh, Vietnam
  • Vu Kim Tuan Department of Mathematics, University of West Georgia, Carrollton, GA 30118, USA

Abstract

n this paper we introduce several iterated convolutions and establish weighted $L_p,\ p>1,-$ norm inequalities for them by using the H\"{o}lder’s inequality and the transform of integrals. Applications to wave and heat equations, Klein-Gordon equation are also considered. Especially, we will see their applications to inhomogeneous differential equations.

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Published

2009-01-08

Issue

Vol. 1 No. 4 (2008)

Section

Articles

How to Cite

[1]
N. D. V. Nhan, D. T. Duc, and V. K. Tuan, “Weighted $L_P-$ Norm Inequalities For Various Convolution Type Transformations And Their Applications”, Armen.J.Math., vol. 1, no. 4, pp. pp. 1–18, Jan. 2009, Accessed: Jan. 19, 2025. [Online]. Available: https://armjmath.sci.am/index.php/ajm/article/view/44