### Abstract

We introduce a class of integral operators related to parametric Marcinkiewicz operators. We present a multiplier formula characterizing the L^{2} boundedness of such class of operators. Also, we prove L ^{p}_{-β} (inhomogeneous Sobolev space)→L^{p} estimates provided that the kernels are in L(logL)(S^{n-1}). In fact, we show that the global parts of the introduced operators are bounded on the Lebesgue spaces L^{p}(1 < p < ∞) while the local parts are bounded on certain Sobolev spaces L^{p}_{-β}.

Original language | English |
---|---|

Pages (from-to) | 56-81 |

Number of pages | 26 |

Journal | Communications in Mathematical Analysis |

Volume | 13 |

Issue number | 2 |

Publication status | Published - 2012 |

### Keywords

- Bessel functions
- Fourier transform
- Marcinkiewicz integrals
- Rough integral operators
- Sobolev spaces
- Triebel-Lizorkin space

### ASJC Scopus subject areas

- Analysis
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics

## Fingerprint Dive into the research topics of 'A class of marcinkiewicz type integral operators'. Together they form a unique fingerprint.

## Cite this

Al-Salman, A. (2012). A class of marcinkiewicz type integral operators.

*Communications in Mathematical Analysis*,*13*(2), 56-81.