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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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Felten M.

Open Mathematics

2007

tom 5

nr 3

505-511

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.

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1 Open Mathematics

1 Felten M.

1 2007

Wyniki wyszukiwania

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