Carfilzomib Plus Belinostat in Relapsed/Refractory NHL

Inclusion Criteria: * Subjects must have histologically confirmed relapsed or refractory non-Hodgkin lymphoma that is not a candidate for standard curative therapy. NHL subtypes include: Diffuse large B-cell lymphoma (DLBCL), Mantle cell lymphoma, Marginal zone lymphoma, Lymphoplasmacytic lymphoma, Peripheral T-cell lymphomas, and Follicular lymphoma of any grade. * Patients must have received at least one prior systemic therapy for lymphoma. A washout period of at least 3 weeks is required from the most recent prior therapy. * Age ≥18 years * ECOG performance status ≤ 2 (Karnofsky ≥ 60%, see Appendix A) * Participants must have organ and marrow function as defined below: * absolute neutrophil count ≥1,000/mcL * platelets ≥75,000/mcL * total bilirubin ≤ 2 × institutional upper limit of normal * AST(SGOT)/ALT(SGPT) ≤ 3 × institutional upper limit of normal * creatinine ≤1.5 × institutional upper limit of normal \--- OR * creatinine clearance ≥45 mL/min/1.73 m2 for participants with creatinine levels above institutional normal. * Participants may have either measurable or non-measurable disease, but in all cases eligible patients must have disease that can be clinically evaluated for improvement or progression. * Patients must have fully recovered from major surgery and from the acute toxic effects of prior chemotherapy and radiotherapy (residual grade 1 toxicity, e.g., grade 1 peripheral neuropathy, and residual alopecia are allowed). * The effects of carfilzomib and belinostat on the developing human fetus are unknown. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of study drug administration. * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Participants who have had chemotherapy or radiotherapy within 3 weeks (8 weeks for radioimmunotherapy) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 3 weeks earlier. * Participants who are receiving any other investigational agents. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to carfilzomib or belinostat * Patients with a systemic fungal, bacterial, viral, or other infection not controlled * Pregnant or lactating patients. * Prior history of another malignancy (except for non-melanoma skin cancer, in situ cervical or breast cancer, or prostate cancer detectable only by PSA) unless disease free for over one year * Uncontrolled intercurrent illness including, but not limited to ongoing or active infection, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. * Congestive heart failure of any severity (NYHA class I-IV) * Any active angina or any unstable angina pectoris or myocardial infarction within one year of study entry. * Left ventricular ejection fraction below the lower limit of normal * Greater than grade 1 peripheral neuropathy at baseline * Congenital long QT syndrome or history of torsades de pointes * Baseline QTc interval \> 500 msec * Concomitant medications required on dosing days that increase risk of torsades de pointes * Subjects with known HIV infection * Active hepatitis B or C infection * Known history of allergy to Captisol® (a cyclodextrin derivative used to solubilize carfilzomib) * Contraindication to any of the required concomitant drugs or supportive treatments, including hypersensitivity to all anticoagulation and antiplatelet options, antiviral drugs, or intolerance to hydration due to preexisting pulmonary or cardiac impairment * Subjects with pleural effusions requiring thoracentesis or ascites requiring paracentesis within 14 days prior to randomization