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Table 1 Special cases of \(\pmb{L^{p,q,\lambda}_{\alpha,\beta, V}}\)

From: Schrödinger type operators on generalized Morrey spaces

θ = 0, α = 0, p = q, 0<λ<1

Morrey space \(L^{p,\lambda}(\mathbb{R}^{n})\) [10]

θ = 0, p = q, 0<λ<1

Morrey type space \(L_{\alpha,V}^{p,\lambda}(\mathbb{R}^{n})\) [6]

α = λ = 0, \(\theta\in\mathbb{R}\), 0<p,q<∞,

Herz spaces \(K_{p}^{\theta,q}\) [11]

α = 0, λ ≥ 0, \(\theta\in\mathbb{R}\), 0<p,q<∞

Morrey-Herz spaces \(MK_{p,q}^{\theta,\lambda}\) [12, 13]