We investigate weak type estimates for maximal functions, fractional and singular integrals in grand Lebesgue spaces. In particular, we show that for the one-weight weak type inequality it is necessary and sufficient that a weight function belongs to the appropriate Muckenhoupt class. The same problem is discussed for strong maximal functions, potentials and singular integrals with product kernels.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc102-0-9,
author = {Vakhtang Kokilashvili and Alexander Meskhi},
title = {One-weight weak type estimates for fractional and singular integrals in grand Lebesgue spaces},
journal = {Banach Center Publications},
volume = {102},
year = {2014},
pages = {131-142},
zbl = {1307.42013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc102-0-9}
}
Vakhtang Kokilashvili; Alexander Meskhi. One-weight weak type estimates for fractional and singular integrals in grand Lebesgue spaces. Banach Center Publications, Tome 102 (2014) pp. 131-142. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc102-0-9/