172 research outputs found
Fractional type Marcinkiewicz integral operators associated to surfaces
In this paper, we discuss the boundedness of the fractional type
Marcinkiewicz integral operators associated to surfaces, and extend a result
given by Chen, Fan and Ying in 2002. They showed that under certain conditions
the fractional type Marcinkiewicz integral operators are bounded from the
Triebel-Lizorkin spaces to . Recently the second author, together with Xue and Yan, greatly weakened
their assumptions. In this paper, we extend their results to the case where the
operators are associated to the surfaces of the form .
To prove our result, we discuss a characterization of the homogeneous
Triebel-Lizorkin spaces in terms of lacunary sequences.Comment: 27page
The Fatou property of block spaces
Around thirty years ago, block spaces, which are the predual of Morrey
spaces, had been considered. However, it seems that there is no proof that
block spaces satisfy the Fatou property. In this paper the Fatou property for
block spaces is verified and the predual of block spaces is characterized
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