Grand Besov-Bourgain-Morrey spaces and their applications to boundedness of operators (Q6564170)

In this titanic study the authors introduce a new class of grand function spaces, called generalized grand Besov-Bourgain-Morrey spaces (for short, generalized grand BBM spaces). They investigate various real-variable properties of generalized grand BBM spaces including embedding properties, completeness, establishment of equivalent quasi-norms (among which quasi-norms expressed by means of Muckenhoupt weights), translation and dilation invariance, convexification, non-triviality, diversity with respect to different exponents, pre-dual spaces characterized in terms of new block spaces, computation of the Calderón product of generalized grand BBM spaces, Gagliardo-Peetre and \(\pm\) interpolation theorems, and boundedness of the fundamental operators of Harmonic Analysis such as the Hardy-Littlewood maximal operator, the fractional integrals, the fractional maximal operators, and the Calderón-Zygmund operators.