Generalizing algebraically defined norms
| Autor: | Jarno Talponen, Alberto Fiorenza |
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| Přispěvatelé: | Fiorenza, A., Talponen, J. |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Pure mathematics
Applied Mathematics General Mathematics Numerical analysis 010102 general mathematics 05 social sciences Ode Cauchy distribution Modular space Fixed point Algebraic construction Musielak–Orlicz space 01 natural sciences Infimum and supremum 0502 economics and business Exponent Non-linear integral equation 0101 mathematics Algebraic number Variable exponent Lebesgue spaces 050203 business & management Mathematics |
| Popis: | We extend the algebraic construction of finite dimensional varying exponent $$L^{p(\cdot )}$$ L p ( · ) space norms, defined in terms of Cauchy polynomials to a more general setting, including varying exponent $$L^{p(\cdot )}$$ L p ( · ) spaces. This boils down to reformulating the Musielak–Orlicz or Nakano space norm in an algebraic fashion where the infimum appearing in the definition of the norm should become a (uniquely attained) minimum. The latter may easily fail, as turns out, and in this connection we examine the Fatou type semicontinuity conditions on the modulars. Norms defined by ODEs are applied in studying such semicontinuity properties of $$L^{p(\cdot )}$$ L p ( · ) space norms with $$p(\cdot )$$ p ( · ) unbounded. |
| Databáze: | OpenAIRE |
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