A new characterization of the conjugates of absolutely continuous operators is presented. We introduce and investigate the concept of positive p-absolutely continuous operators and show in particular that it is a true generalization of absolutely continuous operators. By quantifying the notion of positive p-absolutely continuous operators, we introduce the concept of positive <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$(p,\sigma )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>σ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-absolutely continuous operators and establish the Pietsch domination/factorization theorem for it. By means of positive <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$(p,\sigma )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>σ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-absolutely continuous operators, we introduce the concept of positive <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$((p,\sigma ),(q,\nu ))$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>σ</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mo stretchy="false">(</mo> <mi>q</mi> <mo>,</mo> <mi>ν</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-dominated operators and prove the famous Kwapień’s factorization theorem for it. Finally, we study the maximal properties of the classes of positive <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$(p,\sigma )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>σ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-absolutely continuous operators and positive <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$((p,\sigma ),(q,\nu ))$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mi>p</mi> <mo>,</mo> <mi>σ</mi> <mo stretchy="false">)</mo> <mo>,</mo> <mo stretchy="false">(</mo> <mi>q</mi> <mo>,</mo> <mi>ν</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-dominated operators and show that they are maximal.

Positive $(p,\sigma )$-absolutely continuous operators

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发表日期：

2026年5月22日

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Oussama Djeribia,
Dongyang Chen

摘要

A new characterization of the conjugates of absolutely continuous operators is presented. We introduce and investigate the concept of positive p-absolutely continuous operators and show in particular that it is a true generalization of absolutely continuous operators. By quantifying the notion of positive p-absolutely continuous operators, we introduce the concept of positive $(p,\sigma )$ $(p, σ)$ -absolutely continuous operators and establish the Pietsch domination/factorization theorem for it. By means of positive $(p,\sigma )$ $(p, σ)$ -absolutely continuous operators, we introduce the concept of positive $((p,\sigma ),(q,\nu ))$ $((p, σ), (q, ν))$ -dominated operators and prove the famous Kwapień’s factorization theorem for it. Finally, we study the maximal properties of the classes of positive $(p,\sigma )$ $(p, σ)$ -absolutely continuous operators and positive $((p,\sigma ),(q,\nu ))$ $((p, σ), (q, ν))$ -dominated operators and show that they are maximal.

Positive \((p,\sigma )\)-absolutely continuous operators

摘要