Weighted Inequalities for a Class of Volterra Convolution Operators | Zendy

Stepanov Vladimir D. | Zendy

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Weighted Inequalities for a Class of Volterra Convolution Operators

Author(s) -

Stepanov Vladimir D.

Publication year - 1992

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/jlms/s2-45.2.232

Subject(s) - convolution (computer science) , mathematics , compact space , kernel (algebra) , class (philosophy) , combinatorics , discrete mathematics , pure mathematics , computer science , machine learning , artificial intelligence , artificial neural network

The purpose of this paper is to give necessary and sufficient conditions for the boundedness fromL v p ( R + ) toL u qof Volterra convolution operators of the form k f ( x ) = ∫ 0 x k ( x − y ) f ( y ) d y , where k(x) is a non‐negative non‐decreasing kernel satisfying k(x +y)⩽ D(k(x )+ k(y )) for all x, y ɛ R + . The cases of 1 < p,q < ∞ and 0 < q < 1 < p < ∞ are considered. Also criteria for the compactness of K for 1 < p, q < ∞ are given.

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