Herz-type Sobolev and Bessel potential spaces and their applications

Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz Spaces

“…Since then, the theory of Herz spaces has been significantly developed, and these spaces have turned out to be quite useful in harmonic analysis. For instance, they were used by Baernstein and Sawyer [24] to characterize the multipliers on the classical Hardy spaces and used by Lu and Yang [25] in the study of partial differential equations. More results and further details can be found in [26][27][28].…”

“…For instance, they were used by Baernstein and Sawyer [24] to characterize the multipliers on the classical Hardy spaces and used by Lu and Yang [25] in the study of partial differential equations. More results and further details can be found in [26][27][28]. On the basis of above available results, the theory of the homogeneous Morrey-Herz spaces goes back to Lu-Xu [29] who considered the boundedness of a class of sublinear operators; also see [6,30,31] for more further results.…”

Herz-Type Hardy Spaces Associated with Operators

“…The kernel ( , ) of − satisfies the Gaussian upper bound on R ×R . Motivated by [17,20,37], etc, in this paper, we use the area integral function associated with the operator to define the Herztype Hardy spacė, , (R ). In order to obtain the atomic and molecular decompositions of the Herz-type Hardy space, the ( , , , )-atom and the ( , , , , )-molecule are introduced.…”

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

“…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.…”