Link to the University of Pittsburgh Homepage
Link to the University Library System Homepage Link to the Contact Us Form


Wang, Lifeng (2023) A STUDY ON FUNCTION SPACES. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

PDF (A STUDY ON FUNCTION SPACES - Lifeng Wang (dissertation))
Primary Text

Download (927kB) | Preview


In this dissertation, we investigate the properties of homogeneous function spaces. We study related basic definitions and prerequisite lemmas. We also study useful properties of the famous Hardy-Littlewood maximal function and the Peetre-Fefferman-Stein maximal function for functions whose distributional Fourier transforms have compact supports. Furthermore, we introduce the classical Plancherel-Polya-Nikol'skij inequality for Schwartz functions and then generalize this inequality to the case of sufficiently smooth tempered distributions. We state and prove a complex interpolation theorem for the homogeneous Triebel-Lizorkin spaces. We prove a Fourier multiplier theorem for sequences of functions and deduce another for homogeneous Triebel-Lizorkin spaces. This dissertation provides improved results of function spaces found in the famous literature by Hans Triebel. The first pair of results provides equivalence characterizations of homogeneous Triebel-Lizorkin and Besov-Lipschitz spaces in terms of maximal functions of the mean values of iterated difference. It also furnishes the reader with inequalities in homogeneous Triebel-Lizorkin spaces in terms of iterated difference and in terms of iterated difference along coordinate axes. The corresponding inequalities in homogeneous Besov-Lipschitz spaces in terms of iterated difference and in terms of iterated difference along coordinate axes are also considered.


Social Networking:
Share |


Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairSchikorra,
Committee MemberHajlasz,
Committee MemberManfredi, Juan
Committee MemberSpector, Daniel
Date: 1 September 2023
Date Type: Publication
Defense Date: 28 March 2023
Approval Date: 1 September 2023
Submission Date: 15 June 2023
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 177
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Mathematics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Homogeneous Triebel-Lizorkin space, homogeneous Besov-Lipschitz space, iterated difference, Fourier analysis, Hardy-Littlewood maximal function, Peetre-Fefferman-Stein maximal function.
Date Deposited: 01 Sep 2023 19:05
Last Modified: 01 Sep 2023 19:05


Monthly Views for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item