Abstract. We consider the multidimensional analogues of the Lorentz spaces and weighted Lebesgue spaces. For functions monotone in each variable in these spaces we study integrability properties of their Fourier transforms.

DOI: 10.14232/actasm-015-064-3

AMS Subject Classification (1991): 42B10

Keyword(s): Fourier transform, monotone functions, anisotropic Lorentz spaces, weighted Lebesgue spaces

Received August 25, 2015, and in revised form December 13, 2015. (Registered under 64/2015.)