Abstract
Let K be a locally compact hypergroup. In this paper, among other results we give a sufficient condition for the inclusion LΦ1w (K) * LΦ2w (K) ⊆ LΦ1w (K) to hold. Also, as an application, we provide a new sufficient condition for the weighted Orlicz space LΦw (K) to be a convolution Banach algebra.
Highlights
For each locally compact group G with a sub-multiplicative mapping w, L1(G) and L1w(G) are convolution Banach algebras
If 1 < p < ∞, it is wellknown that the Lebesgue space Lp(G) is a convolution Banach algebra if and only if G is compact [15]
In [17] some necessary and sufficient condition is given for an Orlicz space LΦ(G) to be a convolution Banach algebra, where G is a compactly generated second countable abelian group and Φ belongs to a special class of Young functions
Summary
For each locally compact group G with a sub-multiplicative mapping w, L1(G) and L1w(G) are convolution Banach algebras. In [17] some necessary and sufficient condition is given for an Orlicz space LΦ(G) to be a convolution Banach algebra, where G is a compactly generated second countable abelian group and Φ belongs to a special class of Young functions. Oztop in [10] introduced and studied the weighted Orlicz algebras on locally compact groups, and proved that, if LΦw(G) ⊆ L1w(G), LΦw(G) is a convolution Banach algebra.
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