Abstract
In this paper, we introduce grand variable Herz type spaces using discrete grand spaces and prove the boundedness of sublinear operators on these spaces.
Highlights
The Herz spaces Kqα,p(Rn) and Kqα,p(Rn) were introduced in [10] being known under the names of homogeneous and non-homogeneous Herz spaces and they are defined by the norms p/q 1/p f Kqα,p :=2kαp k∈Z f (x) q dx R2k–1,2k (1)p/q 1/p f Kqα,p := f Lq(B(0.1)) + 2kαp k∈N (2)respectively, where Rt,τ stands for the annulus Rt,τ := B(0, τ ) \ B(0, t)
The aim of this paper is to introduce grand variable Herz spaces Kqα,p),θ (Rn) and obtain the boundedness of sublinear operators on Kqα,p),θ (Rn)
2.2 Herz spaces with variable exponent In this subsection, we introduce variable exponent Herz spaces
Summary
The Herz spaces Kqα,p(Rn) and Kqα,p(Rn) were introduced in [10] being known under the names of homogeneous and non-homogeneous Herz spaces and they are defined by the norms p/q 1/p f Kqα,p :=. Respectively, where Rt,τ stands for the annulus Rt,τ := B(0, τ ) \ B(0, t) These spaces were studied in many papers; see for instance [5, 7, 9, 12,13,14,15, 22] and the references therein. Samko in [33] used variable exponent Herz spaces (with variable parameters), known as continual Herz spaces. Grand Lebesgue spaces on bounded sets have been widely studied. They were introduced in [8, 11], cf [2]. Various operators of harmonic analysis were intensively studied in the last years, cf. [6, 16,17,18,19,20, 27, 28] and the references therein
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