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

WOS: 000371347600006 In this paper, we investigate the boundedness of the Hilbert transform H in the local Morrey-Lorentz spaces [GRAPHICS] , [GRAPHICS] , [GRAPHICS] . We prove that the operator H is bounded in [GRAPHICS] under the condition [GRAPHICS] , [GRAPHICS] . In the limiting case [GRAPHICS] , [GRAPHICS] , we prove that the operator H is bounded from the space [GRAPHICS] to the weak local Morrey-Lorentz space [GRAPHICS] . Also we show that for the limiting case [GRAPHICS] , [GRAPHICS] , the modified Hilbert transform [GRAPHICS] is bounded from the space [GRAPHICS] to the bounded mean oscillation space. Science Development Foundation under Republic of AzerbaijanScience Development Foundation (SDF) - Azerbaijan [EIF-2013-9(15)-46/10/1]; Presidium Azerbaijan National Academy of ScienceAzerbaijan National Academy of Sciences (ANAS) The research of V.S. Guliyev was partially supported by the grant of Science Development Foundation under the President of the Republic of Azerbaijan, Grant EIF-2013-9(15)-46/10/1 and by the grant of Presidium Azerbaijan National Academy of Science 2015.