Lipschitz Transformations and Maurey-Type Non-Homogeneous Integral Inequalities for Operators on Banach Function Spaces
We introduce a method based on Lipschitz pointwise transformations to define a distance on a Banach function space from its norm. We show how some specific lattice geometric properties (<i>p</i>-convexity, <i>p</i>-concavity, <i>p</i>-regularity) or, equivalently,...
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| Format: | Article |
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MDPI AG
2023-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/22/4599 |
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| author | Roger Arnau Enrique A. Sánchez-Pérez |
| author_facet | Roger Arnau Enrique A. Sánchez-Pérez |
| author_sort | Roger Arnau |
| collection | DOAJ |
| description | We introduce a method based on Lipschitz pointwise transformations to define a distance on a Banach function space from its norm. We show how some specific lattice geometric properties (<i>p</i>-convexity, <i>p</i>-concavity, <i>p</i>-regularity) or, equivalently, some types of summability conditions (for example, when the terms of the terms in the sums in the range of the operator are restricted to the interval <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></semantics></math></inline-formula>) can be studied by adapting the classical analytical techniques of the summability of operators on Banach lattices, which recalls the work of Maurey. We show a technique to prove new integral dominations (equivalently, operator factorizations), which involve non-homogeneous expressions constructed by pointwise composition with Lipschitz maps. As an example, we prove a new family of integral bounds for certain operators on Lorentz spaces. |
| first_indexed | 2024-03-09T16:38:16Z |
| format | Article |
| id | doaj.art-7a6de27691f24ea1867a73287e4d4306 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T16:38:16Z |
| publishDate | 2023-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-7a6de27691f24ea1867a73287e4d43062023-11-24T14:54:09ZengMDPI AGMathematics2227-73902023-11-011122459910.3390/math11224599Lipschitz Transformations and Maurey-Type Non-Homogeneous Integral Inequalities for Operators on Banach Function SpacesRoger Arnau0Enrique A. Sánchez-Pérez1Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 València, SpainInstituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 València, SpainWe introduce a method based on Lipschitz pointwise transformations to define a distance on a Banach function space from its norm. We show how some specific lattice geometric properties (<i>p</i>-convexity, <i>p</i>-concavity, <i>p</i>-regularity) or, equivalently, some types of summability conditions (for example, when the terms of the terms in the sums in the range of the operator are restricted to the interval <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></semantics></math></inline-formula>) can be studied by adapting the classical analytical techniques of the summability of operators on Banach lattices, which recalls the work of Maurey. We show a technique to prove new integral dominations (equivalently, operator factorizations), which involve non-homogeneous expressions constructed by pointwise composition with Lipschitz maps. As an example, we prove a new family of integral bounds for certain operators on Lorentz spaces.https://www.mdpi.com/2227-7390/11/22/4599banach function spacelipschitz transformintegral inequality<i>p</i>-convexity<i>p</i>-concavity<i>p</i>-regular operator |
| spellingShingle | Roger Arnau Enrique A. Sánchez-Pérez Lipschitz Transformations and Maurey-Type Non-Homogeneous Integral Inequalities for Operators on Banach Function Spaces Mathematics banach function space lipschitz transform integral inequality <i>p</i>-convexity <i>p</i>-concavity <i>p</i>-regular operator |
| title | Lipschitz Transformations and Maurey-Type Non-Homogeneous Integral Inequalities for Operators on Banach Function Spaces |
| title_full | Lipschitz Transformations and Maurey-Type Non-Homogeneous Integral Inequalities for Operators on Banach Function Spaces |
| title_fullStr | Lipschitz Transformations and Maurey-Type Non-Homogeneous Integral Inequalities for Operators on Banach Function Spaces |
| title_full_unstemmed | Lipschitz Transformations and Maurey-Type Non-Homogeneous Integral Inequalities for Operators on Banach Function Spaces |
| title_short | Lipschitz Transformations and Maurey-Type Non-Homogeneous Integral Inequalities for Operators on Banach Function Spaces |
| title_sort | lipschitz transformations and maurey type non homogeneous integral inequalities for operators on banach function spaces |
| topic | banach function space lipschitz transform integral inequality <i>p</i>-convexity <i>p</i>-concavity <i>p</i>-regular operator |
| url | https://www.mdpi.com/2227-7390/11/22/4599 |
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