The boundedness of Hilbert transform in the local Morrey–Lorentz spaces

Riesz potentials in the local variable Morrey-Lorentz spaces and some applications

“…These spaces are a very natural generalization of the Lorentz spaces such that M loc p,q;0 (R n ) = L p,q (R n ). Recently, in [2,13] and [14] the authors have studied the boundedness of the Hilbert transform, the Hardy-Littlewood maximal operator M and the Calderón-Zygmund operators T , and the Riesz potential I α on the local Morrey-Lorentz spaces M loc p,q;λ by using related rearrangement inequalities, respectively.…”

Maximal and Calderon-Zygmund operators on the local variable Morrey-Lorentz spaces and some applications

“…These spaces are a very natural generalization of the Lorentz spaces such that M loc p,q;0 (R n ) = L p,q (R n ). Recently, in [2,14] and [15] the authors have studied the boundedness of the Hilbert transform, the Hardy-Littlewood maximal operator M and the Calderón-Zygmund operators T , and the Riesz potential I α on the local Morrey-Lorentz spaces M loc p,q;λ by using related rearrangement inequalities, respectively. In [35], the authors give the definition of central Lorentz-Morrey space of variable exponent by the symmetric decreasing rearrangement.…”

Maximal and fractional maximal operators in the Lorentz Morrey spaces and their applications to the Bochner Riesz and Schrodinger type operators

“…Mingione [18], studied the boundedness of the restricted fractional maximal operator M α,B 0 in the restricted Lorentz-Morrey spaces L p,q;λ (B), where B 0 is a given ball and B is any other ball contained in B 0 and containing x. The author derived a general non-linear version, extending a priori estimates and regularity results for possibly degenerate non-linear elliptic problems to the various spaces of Lorentz and Lorentz-Morrey type considered in [1,3,18] and [22]. In [22], Ragusa studied some embeddings between these spaces.…”

“…The local variant of Lorentz-Morrey spaces L p,q;λ (R n ) replacing by B(0, r) instead of B(x, r), so called the local Morrey-Lorentz spaces L loc p,q;λ (R n ) are introduced and the basic properties of these spaces are given in [2]. Recently, in [3,11] and [12], the authors studied the boundedness of some classical operators of harmonic analysis in these spaces.…”