Some criteria for boundedness and compactness of the Hardy operator with some special kernels

Abstract We present necessary and sufficient conditions for boundedness and compactness of Hardy operator (1.4) with kernel (1.3) for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>1</mml:mn> <mml:mo>&lt;</mml:mo> <mml:mi>p</mml:mi> <mml:mo>≤</mml:mo> <mml:mi>q</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mi>∞</mml:mi> </mml:math> . MSC: 26D10, 26D15, 47B07, 47B34, 47B38.

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