Let G be a locally compact group with a fixed left Haar measure. Given Young functions φ
and ψ, we consider the Orlicz spaces $ L^{φ}(G) $ and $ L^{ψ}(G) $ on a non-unimodular …

Let G be a locally compact group. In this paper, for given concave Orlicz functions Φ and Ψ
with limsupt→∞ Φ (t)/t= 0, we prove that the convolution f∗ g exists, for f∈ LΦ (G) and g∈ …

Let G be a locally compact group. In this paper, we show that if G is a nondiscrete locally
compact group, p∈(0, 1) and q∈(0,+∞], then {(f, g)∈ Lp (G)× Lq (G): f∗ g is finite λ-ae} is a …

Let G be a non-compact locally compact group. In this paper we study the size of the set {(f,
g)∈ A× B: f∗ g is well-defined on G} where A and B are normed spaces of continuous …

Abstract Let (Ω, Σ, μ) be a measure space and let φ _1, ..., φ _n and φ be Young functions. In
this paper, we, among other things, prove that the set E={(f_1, ..., f_n) ∈ M^ φ _1 * ⋯ * M^ φ …

Let (X, Σ, µ) be a measure space. If p, q, r∈(0,∞] satisfy 1/p+ 1/q= 1/r, then by a general
version of the Hölder inequality [21], Exercise 1.1. 2, we see that Φ (f, g)= fg∈ Lr for any f∈ …

In this paper, we consider the size of the set\big {(f, g) ∈ ℓ^ p (S) * ℓ^ q (S): ∃\, x ∈ S,\,| f|*|
g|(x)< ∞\big\}(f, g)∈ ℓ p (S)× ℓ q (S):∃ x∈ S,| f|∗| g|(x)<∞, where p ∈ (1,+ ∞) p∈(1,+∞), q …

Abstract For i= 1, 2, 3, let φ i be Young functions,(Ω, μ) a (topological) measure space, E an
ideal of μ-measurable complex-valued functions defined on Ω and E φ i be the …

A subset E of an infinitely dimensional linearly-topological space X is called spaceable if
there is an infinitely dimensional closed subspace Y of X with Y⊂ E∪{0}. The main aim of …

In this paper we first give some preliminaries of Orlicz spaces. Then, using a topological
criterion, we determine the size of subsets in Orlicz spaces on a locally compact group with …