Introduction

Svetlin G. Georgiev ()
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Svetlin G. Georgiev: University of Sofia “St. Kliment Ohridski”, Department of Differential Equations Faculty of Mathematics and Informatics

Chapter Chapter 1 in Theory of Distributions, 2021, pp 1-76 from Springer

Abstract: Abstract In this chapter we introduce the spaces C 0 ∞ $$\mathcal {C}_0^{\infty }$$ , S $$\mathcal {S}$$ , L p, 1 ≤ p ≤∞, and they are deducted some of their properties. They are formulated and proved some variants of the Hölder and Minkowski inequalities. In the chapter is defined the convolution of locally integrable functions and they are proved some of its basic properties. They are introduced some basic facts for cones in ℝ n $$\mathbb {R}^n$$ .

Keywords: Test function; Convolution; Locally integrable function; L p space; Schwartz space (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-81265-2_1

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DOI: 10.1007/978-3-030-81265-2_1

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