Maximal, potential and singular type operators on Herz spaces with variable exponents

Boundedness of some sublinear operators and commutators on Morrey-Herz spaces with variable exponents

“…Next we define the Morrey-Herz space with variable exponents motivated by [1] and [10]. We use the following notation.…”

“…After they were introduced in [6], the theory of these spaces had a remarkable development in part due to its useful applications; we refer to [16] for more details. Herz p(·),q with variable exponent p but fixed α ∈ R and q ∈ (0, ∞] were recently studied by Izuki [9] and these spaces with variable exponents α and p were studied by Almeida and Drihem [1], where they explored the boundedness of a class of classical operators on such spaces. The class of Morrey-Herz spaces MK α,λ q,p(·) (R n ) with variable exponent was initially defined by Izuki in [10] and [11], and the boundedness of both the sublinear operators satisfying a proper size condition and the fractional integrals on MK α,λ q,p(·) (R n ) were proved.…”

“…Condition (1) is satisfied by several classical operators in harmonic analysis, such as Calderón-Zygmund operators, the Carleson maximal operator and the HardyLittlewood maximal operator [1]. The main purpose of this paper is to discuss the boundedness of sublinear operators and their commutators satisfying a proper size condition on Morrey-Herz spaces MK α(·),λ q,p(·) (R n ) with variable exponents α and p.…”

Sobolev's theorem and duality for Herz-Morrey spaces of variable exponent

“…These spaces have attracted more and more attention, in connection with the study of elasticity and fluid mechanics; see [16,33]. On the other hand, variable exponent Morrey or Herz versions were discussed in [4,5,24,26,29].…”

Multilinear Singular Integrals and Commutators on Herz Space with Variable Exponent

“…In [11,12], Izuki independently introduced Herz space with variable exponent , by keeping the remaining two exponents and as constants. Variability of alpha was recently considered by Almeida and Drihem [13] in proving the boundedness results for some classical operators on such spaces. More recently, Samko [14] introduced the generalized Herz-type spaces where all the three exponents were allowed to vary.…”