Carfilzomib Plus Belinostat in Relapsed/Refractory NHL

The investigators are looking for the highest dose of the study drug that can be administered safely without severe or unmanageable side effects in participants that have NHL, not everyone who participates in this research study will receive the same dose of the study drug. The dose the each participant gets will depend on the number of participants who have been enrolled in the study prior and how the dose was tolerated. * Study Drug(s): Both carfilzomib and belinostat will be given through a vein in the participant's arm (IV infusion). Each treatment cycle lasts 28 days (4 weeks). * Carfilzomib will be given on Days 1-2, 8-9, and 15-16 of each cycle. The carfilzomib infusion will be given over about 10 minutes during the first cycle. However if the dose is increased over the course of the trial, or if in one of the groups that joins the study at a higher dose level, the infusion will last about 30 minutes. All participants will remain at the clinic under observation for at least 1 hour following each dose of carfilzomib during Cycle 1 and after the Cycle 2 Day 1 dose. * Belinostat will be given on Days 1-5 of each cycle. The belinostat infusion will be given over about 30 minutes. * Clinical Exams: During all cycles the participant will have a physical exam and will be asked questions about their general health and specific questions about any problems any medications you may be taking. * Pharmacokinetic (PK) blood tests: One of the main reasons for this study is to find the highest dose of the study drug combination that can be used safely without experiencing severe side effects to use for future studies. Once this dose is found (the maximum tolerated dose, or MTD), additional blood samples will be drawn from a small set of participants (about 5 participants total) to learn more about the activity of the study drugs in the body over a period of time, including the ways the study drugs are absorbed, distributed, and then released from the body. If participating in this group (the participant will be informed from the Investigator) these pharmacokinetic (PK) samples will be drawn repeatedly over a period of 24 hours on certain days: Blood samples will be drawn at 0, 15, 30, 60, 90 minutes, and 2, 4, 6, 8 and 24 hours after the study drug dosing on Days 1-2, 4-5, and 9 of Cycle 1. * Scans (or Imaging tests): Tumor assessment by CT or PET CT scans once every 8 weeks (every other cycle).