Martingale transforms in martingale Hardy spaces with variable exponents

Abstract

In this paper, we considered the boundedness of Burkholder's martingale transforms for martingale Hardy spaces with variable exponents. In addition, through martingale transforms, some characterizations of predictable variable exponent martingale Hardy spaces were also provided.

Keywords

• variable exponent
• martingale hardy space
• martingale transform
• doob's maximal inequality
• lipschitz space