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• # Artykuł - szczegóły

## Open Mathematics

2007 | 5 | 3 | 505-511

## Under which conditions is the Jacobi space $$L_{w^{(a,b)} }^p [ - 1,1]$$ subset of $$L_{w^{(\alpha ,\beta )} }^1 [ - 1,1]$$ ?

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### Abstrakty

EN
Exact conditions for α, β, a, b > −1 and 1 ≤ p ≤ ∞ are determined under which the inclusion property $$L_{w^{(a,b)} }^p [ - 1,1]$$ ⊂ $$L_{w^{(\alpha ,\beta )} }^1 [ - 1,1]$$ is valid. It is shown that the conditions characterize the inclusion property. The paper concludes with some results, in which the inclusion property can be detected in relation with estimates of Jacobi differential operators and with Muckenhoupt’s transplantation theorems and multiplier theorems for Jacobi series.

EN

505-511

wydano
2007-09-01
online
2007-04-28

### Twórcy

autor
• Faculty of Mathematics and Informatics University of Hagen

### Bibliografia

• [1] F. Dai and Z. Ditzian: “Littlewood-Paley theory and a sharp Marchaud inequality”, Acta Sci. Math. (Szeged), Vol. 71, (2005), pp. 65–90.
• [2] M. Felten: “Most of the First Order Jacobi K-Functionals are Equivalent”, submitted, pp. 1–12.
• [3] B. Muckenhoupt: “Mean convergence of Jacobi series”, Proc. Amer. Math. Soc., Vol. 23, (1969), pp. 306–310. http://dx.doi.org/10.2307/2037162
• [4] B. Muckenhoupt: “Transplantation theorems and multiplier theorems for Jacobi series”, Mem. Amer. Math. Soc., Vol. 64, (1986), pp. iv–86.