Atomic decompositions and John-Nirenberg theorem of grand martingale Hardy spaces with variable exponents (Q2071907)

Summary: Let \(\theta\geq0\) and \(p(\cdot)\) be a variable exponent, and we introduce a new class of function spaces \(L_{p(\cdot), \theta}\) in a probabilistic setting which unifies and generalizes the variable Lebesgue spaces with \(\theta=0\) and grand Lebesgue spaces with \(p(\cdot)\equiv p\) and \(\theta=1\). Based on the new spaces, we introduce a kind of Hardy-type spaces, grand martingale Hardy spaces with variable exponents, via the martingale operators. The atomic decompositions and John-Nirenberg theorem shall be discussed in these new Hardy spaces.