Intrinsic square functions on the weighted Morrey spaces

Abstract

a b s t r a c tIn this paper, we will study the boundedness properties of intrinsic square functions including the Lusin area integral, Littlewood-Paley g-function and g * λ -function on the weighted Morrey spaces L p,κ (w) for 1 < p < ∞ and 0 < κ < 1. The corresponding commutators generated by BMO(R n ) functions and intrinsic square functions are also discussed.

Weighted Morrey Spaces Related to Certain Nonnegative Potentials and Riesz Transforms

“…Note that this definition does not coincide with the one given in [7] (see also [11] for the unweighted case), but in view of the space BMO ρ,∞ (R d ) defined above it is more natural in our setting. Obviously, if we take θ = 0 or V ≡ 0, then this new space is just the weighted Morrey space L p,κ (w), which was first defined by Komori and Shirai in [6] (see also [12]). Definition 2.2.…”

An intrinsic square function on weighted Herz spaces with variable exponent

“…An intrinsic square function is one of the remarkable operators in modern real analysis. Many researchers have studied characterizations of general function spaces via intrinsic functions ( [11,23,24,25,26,27,28,29]). In particular we focus on the work [25] by Wang where the boundedness of some intrinsic functions including S β on weighted Herz spaces has been proved under proper assumptions on every exponent and weight.…”

Intrinsic Square Functions on Morrey and Block Spaces with Variable Exponents

“…The boundedness result of the intrinsic square function has been extended to the other important function spaces in harmonic analysis. The boundedness of the intrinsic square function on weighted Morrey spaces, weighted weak Hardy spaces and weighted Hardy spaces were established in [30][31][32][33][34], respectively. It had been further generalized to the Musielak-Orlicz Hardy spaces and Musielak-Orlicz Morrey and Campanato spaces in [26][27][28].…”

“…The results obtained in Sect. 4 also generalize the boundedness of the scalar-valued and vector-valued intrinsic square functions on the classical Morrey spaces in [32] and [34,Theorem 1], respectively.…”